Measurement Workbook

Edition 2020-21

Electrical & Electronics Measurements PEN-Drive / G-Drive Course & LIVE Classroom Program

Workbook Electrical Engineering Electrical & Electronics Engineering Instrumentation Engineering

GATE / ESE / PSUs

Electrical & Electronic Measurements PEN-Drive / G-Drive Course & LIVE Classroom Program 

Workbook  EE / EEE / IN

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Edition 

:  2020-21 

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GATE Syllabus Electrical Engineering (EE) : Bridges and Potentiometers, Measurement of voltage, current, power,  energy  and  power  factor;  Instrument  transformers,  Digital  voltmeters  and  multimeters,  Phase,  Time and Frequency measurement; Oscilloscopes, Error analysis.  Instrumentation  Engineering  (IN)  :  SI  units,  systematic  and  random  errors  in  measurement,  expression of uncertainty ‐ accuracy and precision index, propagation of errors. PMMC, MI and  dynamometer  type  instruments;  dc  potentiometer;  bridges  for  measurement  of  R,  L  and  C,  Q‐ meter. Measurement of voltage, current and power in single and three phase circuits; ac and dc  current  probes;  true  rms  meters,  voltage  and  current  scaling,  instrument  transformers,  timer/counter,  time,  phase  and  frequency  measurements,  digital  voltmeter,  digital  multimeter;  oscilloscope, shielding and grounding. 

ESE Syllabus Electrical Engineering (EE) : Principles of measurement, accuracy, precision and standards;  Bridges and potentiometers; moving coil, moving iron, dynamometer and induction type  instruments,  measurement  of  voltage,  current,  power,  energy  and  power  factor,  instrument transformers, digital voltmeters and multi‐meters, phase, time and frequency  measurement, Q‐meters, oscilloscopes, potentiometric recorders, error analysis, Basics of  sensors, Transducers, basics of data acquisition systems     

 

       

Table of Contents Sr.  Chapter  

Pages 

1. 

AC Bridge ………………………………………………...…….…..…..…. 

1 to 10 

2. 

Basic Instruments …………………………………………..……….…. 

11 to 22 

3. 

Measurement of Power…………………………………….…....…. 

23 to 35 

4. 

Measurement of Energy (Only EE) ………….…………………. 

36 to 38 

5. 

Measurement of Resistance …………………………….……..…. 

39 to 43 

6. 

Potentiometer …...………………..………………………..…..…..…. 

44 to 46 

7. 

Instrument Transformer …..……………………………………..…. 

47 to 50 

8. 

Error Analysis …………………………………………………..……..…. 

51 to 57 

9. 

Q ‐ Meter ………………………………………………………...……..…. 

58 to 62 

10.  Cathode‐Ray Oscilloscope (CRO) …..…………………….…..…. 

63 to 73 

11.  Digital Volt Meter (DVM) …..……………………………….…..…. 

74 to 76 

   

 

   

 

Video Lecture Information Sr. 0

Lecture Name

Duration

How to Study Analog Electronics ?

AC Bridge 1

Introduction to Electrical & Electronics Measurements

0:34:20

2

Introduction to Bridge Network

0:26:38

3

Wheatstone Bridge (Part 1)

0:56:55

4

Wheatstone Bridge (Part 2)

0:48:02

5

Concept of Sensitivity

0:26:55

6

Workbook Questions on Wheatstone Bridge

1:05:11

7

Introduction to AC Bridge

0:34:42

8

Arm Combinations

0:41:51

9

Source & Detectors

0:17:49

10

Maxwell Bridge

0:27:35

11

Hay's Bridge

0:34:18

12

Anderson Bridge

0:28:53

13

Owen's Bridge

0:42:03

14

Capacitance Measurement by Desauty's Bridge

0:41:09

15

Schering Bridge

0:16:27

16

Application of Schering Bridge

0:24:23

17

Frequency Measurement by Wein Bridge

0:35:10

18

Wagner earthing device

0:17:34

19

Workbook Questions

1:10:07

Basic Instruments 1

Introduction to Basic Instruments

0:43:45

2

Concept of Torque

0:09:37

3

Permanent Magnet Moving Coil

0:21:41

4

Concept of Sensitivity

0:14:40

5

Moving Iron Instrument

0:38:43

6

Electromagnetic Moving Coil Instruments

0:15:43

7

Electrostatic Voltmeter

0:12:57

8

Workbook Questions

1:18:04

Measurement of Power 1

Measurement of Power by using matlab

0:14:51

2

Measurement of Power by using Voltmeter-Ammeter Method

0:18:17

3

Concept of Power in AC Circuit

0:52:08

4

Introduction to Measurement of Power in AC Circuit

0:06:31

5

Working Principle of Electrodynamometer type wattmeter

0:17:00

     

6

Concept of Deflecting Torque in Wattmeter

0:08:00

7

Basic application of Wattmeter in single phase AC circuit

0:46:24

8

Blondel's Theorem

0:09:35

9

Measurement of 3 phase Power by using One Wattmeter Method

0:37:06

10

Measurement of 3 phase Power by using Two Wattmeter Method for star load

0:42:29

11

Analysis of Two Wattmeter Method

0:08:50

12

Measurement of 3 phase Power by using Two Wattmeter Method for delta load

0:26:36

13

Measurement of 3 phase Power by using Three Wattmeter Method

0:07:56

14

Measurement of Reactive Power in 3 phase circuit

0:20:22

15

Errors in wattmeter reading due to connections

0:53:47

16

Error in wattmeter

0:30:34

17

Low power factor wattmeter

0:11:48

18

Workbook Questions 1-3

1:01:02

19

Workbook Questions 4-7

0:46:40

20

Workbook Questions 8-11

0:42:18

Measurement of Energy 1

Introduction to Energymeter

0:11:15

2

Construction and Working of Energymeter

0:25:02

3

Errors & Compensation in Energymeter

0:33:13

4

Workbook Questions

0:39:56

Measurement of Resistance 1

Introduction to Resistance

0:24:40

2

Measurement of Low Resistance

0:15:58

3

Measurement of Medium Resistance

0:41:53

4

Measurement of High Resistance

0:32:20

5

Worbook Questions

0:26:44

Potentiometer 1

Introduction to Potentiometer

0:16:16

2

Measurements of unknown voltage source by using Potentiometer

0:37:08

3

Applications of Potentiometer

0:19:48

4

Workbook Questions

0:50:24

Error Analysis

 

1

Introduction to Error Analysis

0:25:08

2

Types of Error

0:20:58

3

Characteristics of Instruments (Part 1)

1:13:31

4

Characteristics of Instruments (Part 2)

1:04:51

5

Random Error Analysis

0:18:35

6

Mathematical Operations including Errors

0:32:25

7

Statistical Error Analysis

0:43:36

8

Standard Deviation & Uncertainity

0:22:39

     

9

Workbook Questions 1-4

0:52:42

10

Workbook Questions 5-9

0:45:33

1

Introduction to Q Meter

0:29:07

2

Applications of Q Meter

0:32:04

3

Measurements of Capacitance

0:10:55

4

Measurements of Distributed Capacitance

0:12:07

5

Workbook Questions

0:39:10

Q-Meter

Digital Voltmeter (DVM) 1

Introduction to DVM

0:11:04

2

Working of DVM

0:22:08

3

Concept of Resolution

0:21:55

4

Types of DVM

0:29:22

5

Analysis of Formulas in DVM

0:31:59

6

Workbook Questions

0:19:37

Electrodynamometer 1

Concept of Torque in Electrodynamometer

0:47:34

2

Working of Electrodynamometer

0:16:01

Timer & Counter

               

1

Introduction to Timer & Counter

0:14:30

2

Period Mode of Operation

0:09:59

3

Frequency Mode of Operation

0:07:04

4

Workbook Questions

0:03:21

   

           

1

AC Bridge

Formulas & Logics 1.1

Generalized Circuit : A general circuit of bridge with complex impedances connected in branch shown in below figure. V1

Z

B

q1 Ð 1

V3 I2

Z

2

2

I1

A

Z

3

C

D

I3

I

Ð q

Ð q

q4 Ð Z4 V4

I4

3

V2

D VAC

Fig. Circuit diagram

Z1Z 4  Z 2 Z 3

1  4  2  3 1.2 1. 3. 1.2.1

Measurement of Self-Inductance (L) Maxwell L-C bridge : Medium Q(1  Q  10) Anderson bridge : Low Q (Q  1)

2. Hay’s bridge : High Q (Q  10) 4. Owen’s bridge : relative permeability

Maxwell (L-C) bridge : V1

V3 I3

L1

R3

R1 I1

I

D

I2 R2

R4 I4

V2

C4 V4

VAC

Fig. Circuit diagram

GATE ACADEMY®

2

Electrical & Electronic Measurements [Workbook]

R2 R3 R4

R1 

L1  R2 R3C4 Quality factor of coil (Q) : Q

L1 R2 R3C4   C4 R4 R2 R3 R1 R4

1.2.2 Hay’s bridge : V1

V3 I3

L1

R3

R1 I1

D ID = 0

I2

I

C4

R4

R2

I4

V2

V4 VAC

Fig. Circuit diagram Quality factor of coil :

R2 R3C4 1  2 R42C42 1 L  2  Q 2  R2 R3C4C4 C4 R4 R1 1  2 R42C42

L1  R2 R3C4 R1  2 R2 R3 R4C42

1.2.3 Anderson Bridge : V1

(Test) L1

A

I1

R1

r1

V3

B I1

R3

D IC

E

I2

r

I

R2 V2

I3

D

C

R4 I4 V4

VAC

Fig. Circuit diagram

F

GATE ACADEMY®

3

AC Bridge

R1 

R2 R3  r1 R4

L1 

CR3  R2 (r  R4 )  rR4  R4

1.2.4 Owen’s Bridge : V1

V3 I3

L1

R3

R1 I1

D

I2 R2

I

I4

C2 V2

C4 V4

VAC

Fig. Circuit diagram

L1  R2 R3C4 R1 

R3C4 C2

1.2.4 (a) Modified Owen’s Bridge : L1

R3

D R2

C4

C2

CB

LB

VDC r

I

VAC

Fig. Circuit diagram

L1  R2 R3C4 r 

1.3

R2 R3C4 l N 2 0 A

Capacitance Measurement

1. De-Sauty’s bridge 2. Schering bridge

GATE ACADEMY®

4

Electrical & Electronic Measurements [Workbook]

1.3.1 De-Sauty’s Bridge : V1

V3 r1

C1

I3 R3

R1 I1

D

I2 R2

I

C2 V2

R4

I4

r2

V4 VAC

Fig. Circuit diagram RC C1  4 2 R3

R ( R  r )  R1 r1  3 2 2 R4 1.3.2 Schering Bridge

V1

V3 I3

r1

C1

R3

I1

D

I2 C2

I

R4

I4

C4

V2

V4 VAC

1.4

Fig. Circuit diagram RC R4C2 C1  r1  3 4 C2 R3 Measurement of Frequency (Wein’s Bridge) V1

V3 I3

C1

R3

R1 I1 I2

I

C2

D I4

R2 V2

R4 V4

VAC

Fig. Circuit diagram 1 f  2 RC

GATE ACADEMY®

5

AC Bridge

Objective & Numerical Ans Type Questions :

Q.1

R1

R3

jX 1

Figure shows a balanced ac bridge is excited by a voltage source of fixed frequency. The impedance of unknown arm Z is

R4

R2

- jX 4

(A) First adjust R4 and then adjust R1

D

(B) First adjust R2 and then adjust R3

Z

(C) First adjust R2 and then adjust R4 (D) First adjust R4 and then adjust R2

(A) R and L in series

[GATE-2008, IISc-Bangalore]

(B) R and C in series

Common Data Question For Q.4 and Q.5

(C) R and C in parallel

Q.4

(D) R and L in parallel [GATE-1993, IIT-Bombay]

Q.2

The ac bridge shown in the figure is used to measure the impedance Z. B

bridge.

3KW

C

D

15V + -

15.91mH

Z

300 W

(B) (0  j200) 

(C) (260  j200) 

(D) (260  j200) 

G

+

4KW

VAN -

When R is 2 K  R , VAN is

Q.5

(A) 6 V (B) 6.0024 V (C) 6.0038 V (D) 6.005 V The value of R is approximately (A) 2.8  (B) 3.4  (C) 5.2 

[GATE-2008, IISc-Bangalore]

A bridge circuit is shown in the figure below. Which one of the sequence given below is most suitable for balancing the bridge?

6KW

A

N

If the bridge is balanced for oscillator frequency f = 2 kHz, then the impedance Z will be (A) (260  j0) 

Ig

R

D

Q.3

[GATE-2008, IISc-Bangalore]

300 W

Oscillator A

scale resolution of 1 mm. Let R be minimum increase in R from its nominal value of 2 K that can be detected by this

0.398 mF

500 W

In the Wheatstone bridge shown below the galvanometer G of current sensitivity of 1 Α/mm , a resistance of 2.5 K and a

(D) 12  [GATE-2008, IISc-Bangalore]

Q.6

The resistance and inductance of an inductive coil are measured using an AC bridge as shown in figure. The bridge is to be balanced by varying the impedance Z 2 .

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

6

Coil

R1 R4

R1

L4

R2

C2

D C1

Z

Z2 R3

For obtaining balance Z 2 should consist of element : (A) R and C

(B) R and L

(C) L and C

(D) Only C [GATE-2014, IIT-Kharagpur]

Q.7

If the deflection of the galvanometer in the bridge circuit shown in the figure is zero, then the value of Rx in ohms is _______  .

(A) Resistance only (B) Capacitance only (C) Resistance and capacitance in parallel (D) Resistance and inductor in series Q.10 The bridge circuit in figure is balanced the value of current I is I

1K

V0

Vi 100Ω

2V

200Ω

100Ω

4K

50Ω 100Ω G Rx 100Ω

(A) 2 mA (C) 5 mA

2K

(B) 4 mA (D) 6 mA [GATE-1999, IIT-Bombay]

2V

[GATE-2015, IIT-Kanpur]

Q.8

In the bridge circuit shown in figure when XC  1, then voltmeter reads R

R 10 V

Q.11 The bridge circuit shown in the figure below is used for the measurement of an unknown element Z X . The bridge circuit is best suited

when Z X is a

R D

R

(A) Low resistance (C) Low Q inductor XC

[GATE-2011, IIT-Madras] Q.12

(A) 5 V (C) 2.5 V

(B) 0.0 V (D) 10 V [GATE-1996, IISc-Bangalore]

Q.9

The ac bridge in figure remains balance if Z comprises of [GATE-1998, IIT-Delhi]

(B) High resistance (D) Lossy capacitor

The parallel resistance-capacitance bridge shown below has a standard capacitance value of C1  0.1 F and a resistance value of R3  10 k . The bridge is balanced at a supply frequency of 100 R1  375 k , R3  10 k

Hz

for and

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7

R4  14.7 k . The value of the dissipation D  1/ (RP CP )

AC Bridge

In the Maxwell bridge as shown in given

Q.3

parallel

figure, the values of resistance Rx and

combination of CP and RP is ________.

inductance Lx of a coil are to be calculated

(Answer should be rounded off to three decimal places). [GATE-2019, IIT-Madras]

after balancing the bridge. The component

factor

of

the

values are shown in the figure at balance. The values of Rx and Lx will respectively be

Rp

R1 C1

LX

Cp

RX

R3

2000 W

D

R4

0.05mF 750 W

Practice (objective & Num Ans) Questions :

Q.1

In the Wheatstone bridge shown in the given figure, if the resistance in each arm is increased by 0.05% then the value of Vout will be 10 kW

5 kW

10 V

Q.2

(B) 5 mV

(C) 0.1 V

(D) Zero

In the bridge given in figure, the reading of

10W

10W

20W I 1

Q.5 10V

(C) 37.5 ,75 mH

(D) 75 , 75 mH

List II

A

Anderson Bridge

1.

Frequency

B

Kelvin Double Bridge

2.

Resistance

C

Schering Bridge

3.

Inductance

D

Wien Bridge

4.

Capacitance

Codes :

the high impedance voltmeter is 20W

(B) 75 ,150 mH

List I

16 kW

(A) 50 mV

(A) 375 , 75 mH

Match List-I (Bridges) with List-II (Quantity measured) and select the correct answer using the codes given below the lists

Q.4

Vout

8 kW

4000 W

A

B

C

D

(A)

3

2

1

4

(B)

3

2

4

1

(C)

2

1

3

4

(D)

2

3

4

1

best

suited

Wien bridge is measurement of

(A) Zero

(B) 6.66V

(A) Frequency

(B) Capacitor

(C) 4.20 V

(D) 3.33 V

(C) Inductor

(D) Resistor

for

the

Electrical & Electronic Measurements [Workbook]

Q.6

P Q

R

S

The items in List - I represent the various types of measurements to be made with a reasonable accuracy using the suitable bridge. The items in List - II represent the various bridges available for this purpose. Select the correct choice of the item in List II for the corresponding item in List - I from the following : List I Resistance in the milli-Ohm range Low values of Capacitance

(B) 50 mH in series with 50  (C) 50 nF in series with 10 k (D) 50 nF in parallel with 5 k Q.8

2.

3.

by introducing a small voltage v. The value of  R is R1 = R

R = R2

D v

R4 = R + DR

Wien’s Bridge

4.

The resistance values of the bridge circuit shown in figure are R1  R2  R3  R

and R4  R   R . The bridge is balanced

List II Wheatstone Bridge Kelvin Double Bridge Schering Bridge

1.

Comparison of resistances which are nearly equal Inductance of a coil with a large time constant

GATE ACADEMY®

8

R = R3

E

v E R 2v (C) E  2v

(A)

Hay’s Bridge Carey–Foster Bridge

5. 6.

Rv E v Rv (D) E  2v

(B)

Assignment (objective & Num Ans) Questions :

Q.7

Codes : P Q R S (A) 2 3 6 5 (B) 2 6 4 5 (C) 2 3 5 4 (D) 1 3 2 6 In the ac bridge shown in figure the detector D reads zero. Then Z is made of

Q.1

Q.2

100 nF 500 W 10 KW

Hay’s bridge is suitable for the measurement of which one of the following? (A) Inductance with Q < 10 (B) Inductance with Q > 10 (C) Capacitance with high dissipation (D) Capacitance with low dissipating factors The Wheatstone bridge method of measuring resistance is ideally suited for the measurement of values in the range of (A) 0.001 to 1  (B) 0.1 to 100 

D

(C) 100  to 10 k 1KW

Z

(D) 100 k to 10 M Q.3

Vs = 10 cos 314t

(A) 50 mH in parallel with 50 

The value of a resistance as measured by a Wheatstone bridge is 10.0 k using a voltage source of 10.0 V. The same resistance is measured by the same bridge using 15.0 V. The value of resistance is

GATE ACADEMY®

Q.4

9

(A) 15.0 k

(B) 15.5 k

(C) 16.6 k

(D) 10.0 k

AC Bridge 2R

R

D

A Wheatstone bridge has got three resistances taken in clockwise direction as 120  , 150  and 150  . The value of the

R

R C

C

fourth resistance for null balance would be (A) 150  (B) 120  (C) 300  Q.5

(D) 750 

V, w0

Q.8

The bridge circuit shown can be used to measure unknown lossy capacitor C x with resistance Rx . At balance. C1

The unbalanced voltage of the Wheatstone bridge, shown in the figure is measured using a digital voltmeter having infinite input impedance and a resolution of 0.1 mV. If R  1000  , then the minimum value of

R in  to create a detectable unbalanced voltage is___________.

R2 R1

RX = R + DR

R

G mV

Rx

C3 Cx

R

Q.6

Q.7

(A) Rx 

C1 R R2 and Cx  1 C3 C3 R2

(B) Rx 

C3 R R1 and Cx  2 C3 C1 R1

(C) Rx 

R1 C R2 and Cx  1 R2 C2 R1

R –

+ 2V

Q.9

The inductance of a coil is measured using the bridge shown in the figure. Balance ( D  0) is obtained with C1  1nF,

R1  2.2 M, R2  22.2 k, R4  10 k.

(D) Rx  R2 and Cx  C3

The value of the inductance Lx (in mH) is

where R1, R2 , C1 and C3 can be assumed

___________.

ideal components. Inductance of a coil having Q value in the range of (1< Q < 10), can be measured by using (A) Hay's bridge (B) De Sauty’s bridge (C) Maxwell's bridge (D) Carry Foster's bridge In the a.c. bridge, shown in the figure,

R  103  and C  107 F. If the bridge is balanced at a frequency 0 , the value of 0 in rad/s is_______.

C1 R2 R1 Vs

~

D Lx R4 Rx

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

10

Answer Keys

Objective & Numerical Answer Type Questions 1.

C

2.

A

3.

C

4.

B

5.

B

6.

B

7.

33.33

8.

A

9.

C

10.

D

11.

C

12.

0.035 to 0.045

5.

A

5.

A

Practice (Objective & Numerical Answer) Questions 1.

D

2.

D

3.

A

6.

A

7.

B

8.

D

4.

B

Assignment (Objective & Numerical Answer) Questions 1.

B

2.

C

3.

D

4.

B

6.

C

7.

10000

8.

0.2

9.

222 

2

Basic Instruments

Formulas & Logics 2.1

Permanent Magnet Moving Coil (PMMC) Instrument : 0 1

2

3 4

Scale

5 6

7

I Spring

N

V

B

Permanent magnet

Spring

S

Moving coil

Fig. Circuit diagram Force exerted on the coil is,

F  NBIl sin 

[   90]

Deflecting torque will be,

Td  F  b  NBIlb Td  ( NBA) I  GI

[ G  NBA ]

Where, n  number of turns of coil, B  Magnetic flux density, A  Area of coil  l  b ,

At balance condition :

Td  Tc  K   GI 

GI   I K

K  Spring constant

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

12

Deflection  current, q

I Fig. Relation between deflection and current

2.2

Enhancement of Meters : Rsh 

Where, m  2.3

Rm m 1

I

[ Rsh  Rm ]

V

Ish Rsh

Im Rm

I  Multiplying factor/Multiplication factor Im

Voltmeters : For Enhancement of voltmeter, a resistance made of manganin is connected in series to the meter called series multiplier resistance and the value of this resistance is very high compared to meter resistance. Im = Ifsd Rs

V Rm

Vm

Fig. Circuit diagram Where, V  Voltage to be measured, I fsd  I m  Full scale deflection current 

RS  Series resistance,

V Rm  Rs

Rm  Meter resistance.

Apply voltage division rule, Vm 

V .Rm Rm  Rs

V R  Rs R  Rs  m m m Vm Rm Rm

[ m  Multiplication/Multiplying factor]

Rs  Rm (m  1) Voltage sensitivity : SV 

1 I fsd



Rm  Rs Ω/V V

GATE ACADEMY®

2.4

13

Basic Instruments

Application of PMMC : 2.4.1 Half wave rectifier meter : Rs

Rf

I Vs = Vm sin wt

Rm

PMMC

Fig. Circuit diagram

Where, Rs  Source resistance, R f  Forward diode resistance,

Rm  Resistance of PMMC instrument I average 

0.45Vrms Rs  R f  Rm

…(i)

For d.c. input signal, I mdc 

Vdc Rm  Rs  R f

…(ii)

I average  0.45 I m dc

Since, average current through the meter is 0.45 times the current for d.c. input. Therefore sensitivity of half wave rectifier is 0.45 times that of d.c. sensitivity S ac

1 2

 0.45 S dc

2.4.2 Full wave rectifier type meter : Rs Vs  Vm sin  t

I

PMMC meter

Fig. Circuit diagram

I average 

2 2Vrms 0.9Vrms  [ Rs  2 R f  Rm ] Rs  2 R f  Rm

…(i)

For DC input,

I mdc 

Vdc Rs  2R f  Rm

…(ii)

I average  0.9 I m dc

a.c. sensitivity for full wave rectifier type instrument is 0.9 times the d.c. sensitivity.

2.5 2.6

GATE ACADEMY®

14

Electrical & Electronic Measurements [Workbook]

Moving Iron (MI) Instruments : Principle : Moving iron type instrument may be attraction type or repulsion type.These are based on the principle of minimum reluctance. Torque Equation : 1 dL Deflecting torque, Td  I 2 2 d Controlling torque, Tc  K 

At balance, Tc  Td 1 dL K  I 2 2 d 2  I Since   I 2 , therefore scale is non-linear. q

2.7

I Fig. Relation between deflection and current Electro Dynamometer Type Instrument (Electromagnetic Moving Coil Instrument)

I2 (DPST)

F.C.1

F.C.2

I2

I1

I1 I1

1  Supply

I2

( I1  I 2 )

I1

L (Lag O Power A D Factor)

Fig. Circuit Diagram 2.8

Torque Equation : dM d Where, i1  instantaneous current through moving coil,

Instantaneous torque, Td  i1i2

i2  instantaneous current through fixed coil M  Mutual inductance between fixed and moving coil, K  Spring constant,

GATE ACADEMY®

15

At balance condition,

Tc  Td dM d

K   i1i2

For D.C. application,

i1  i2  I K  I 2

dM d

 I2 For A.C. application, i1  I m1 sin t i2  I m2 sin(t  )

Td  I m1 I m2 sin(t )sin(t  )

dM d

Average deflecting torque, Td avg 

1 T Td d t T 0

Td avg  I1I 2 cos 

dM d

Where I1 and I 2 are rms value of current through moving coil and fixed coil. 2.9

Applications of electro dynamometer (EMMC) instrument :

verage deflecting torque, Td avg  I1I 2 cos 

dM d

(i) I1  I 2  I , Td  I 2 : Ammeter (ii) I1  I 2  (iii) I1 

V , Td  V 2 : Voltmeter R

V , I 2  I , Td  VI cos  : Wattmeter R

(iv) Power factor meter (v) Frequency meter (vi) Meggar (For measurement of high resistance)

Basic Instruments

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

16

(A) 50 

(B) 25 

The current i(t ) passing through 10

(C) 5 

(D) 2.5 

resistor a shown in figure (i) as a wave form as shown figure (ii). The reading of dc voltmeter meter is connected across 10

[GATE-1997, IIT-Madras] For the two square inputs in the figure, the PMMC meter will read, the maximum when the phase difference b/w them is ________

Objective & Numerical Ans Type Questions :

Q.1

Q.5

resistor is ________V. [GATE-1991, IIT-Madras] 10 W

I

XOR Gate

X T

pmmc Y T

DC voltmeter

Fig. (i)

(A) 0

(B)

i (t )

(C)

12A 5A

Q.6 T

Q.2

2T

t

3T

[GATE-1998, IIT-Delhi] A dc voltmeter has a sensitivity of 1000 /Volt when it measure half of full

voltmeter is (A) 100 mA (C) 0.5 mA

Fig. (ii) The saw tooth voltage waveform shown in figure is fed to a moving iron voltmeter. Its reading would be close to________

(B) 1 mA (D) 50 mA [GATE-1998, IIT-Delhi] Two 100 A full scale PMMC meters are employed to constant a 10 V and 100 V scale voltmeter. These meters will have figure of merits (sensitivities) as (A) 10K/V and 10K /V

100 V

20 ms

Q.4

(D) T

scale in 100V range, the current through the

Q.7

Q.3

T 2

T 4

40 ms

(B) 100K/V and 10K/V

t

[GATE-2014, IIT- Kharagpur] Two 100 V full scale PMMC type dc voltmeter having figure of merits (FOM) of 10 K /V and 20 k/V are connected in

series. The series combination can be used to measure a maximum dc voltage of ________. [GATE-1994, IIT-Kharagpur] An ammeter with input resistance of 50 gives full scale deflection for 50 A current. The input resistance of a 0 – 1mA ammeter obtained by connecting a shunt across the 0  50 A meter will be

(C) 10K/V and 100K/V (D) 10 K /V and 1K /V Q.8

[GATE-1999, IIT-Bombay] The insulation level for a 5 Amp full scale rectifier type ammeter is specified as 2.5 kV. It is then safe to use the meter with a potential difference of upto 2.5 kV between (A) The terminal of the meter (B) Case and the ground (C) Both the terminal and the case (D) One of the terminal and the ground. [GATE-2003, IIT-Madras]

GATE ACADEMY®

Q.9

17

The 5 V Zener diode in below figure is ideal and the ammeter (A), of full-scale 1 mA, has an internal resistance of 100  . The circuit shown, with terminal 1 positive, functions as a Rm = 100 W A

1

Basic Instruments

(A) 63.56 

(B) 69.93 

(C) 89.93 k

(D) 141.3 k [GATE-2003, IIT-Madras]

Q.12 An ideal diode has been connected across a 10 , 100mA , center-zero PMMC meter as

shown in figure. The meter will read 990 W

Vz = 5 V Rs = 900 W 100sin 314t

+

10 W 100 mA

~

-

2

(A) 0 –1 V DC voltmeter (B) 0 – 1 mA DC ammeter (C) 0 – 6 V DC voltmeter (D) 0 – 5 V AC voltmeter [GATE-2003, IIT-Madras] Q.10 The inductance of a certain moving iron 2 ammeter is expressed as L  10  3  H 4 where  is the deflection in radian from the zero position. The control spring torque is 25 10 6 Nm/radian .

constant

The

deflection of the pointer in radian when the meter carries a current of 5A is (A) 2.4 (B) 2.0 (C) 1.2 (D) 1.0 [GATE-2003, IIT-Madras] Q.11 A rectifier type ac voltmeter consists of a series resistance Rs an ideal full wave rectifier bridge and a PMMC instrument as shown in figure. The internal resistance of the instrument is 100 and a full scale deflection is produced by a dc current of 1 mA. The value of Rs required to obtain full scale deflection with an ac voltage of 100V (rms) applied to the input terminal is Rs

100 V ac input

pmmc milli ammeter

~

(A) 100mA

(B)  31.8mA

(C)  31.8mA

(D)  67.3mA [GATE-2004, IIT-Delhi]

Q.13 A 1000 V dc supply has two 1- core cables as its positive and negative leads : their insulation resistance to earth are 4M and

6M respectively as shown in the figure. A voltmeter with resistance 50K is used to measure the insulation of the cable. When connected b/w positive core and earth, the voltmeter reads 1000 V

K 4 MW

6 MW

V

(A) 8V

(B) 16V

(C) 24V

(D) 40V [GATE-2005, IIT-Bombay]

Q.14 The 100 A full scale current and 100

coil resistance PMMC meter is connected in the circuit shown in the adjoining figure. The op-amp is ideal. The voltage Vi (t )  1.0sin314t . Assuming the source impedance of Vi (t ) to be zero, the ammeter will indicate a current of

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

18 1K

A

14.14sin 314t

(A) 100 A

(B) 70.7 A

(C) 63.7 A

(D) 31.8 A [GATE-2010, IIT-Guwahati]

Q.15 An analog voltmeter uses external/multiplier setting. With a multiplier setting of 20K

it reads 440 V and with a multiplier setting of 80K , it reads 352 V. for a multiplier setting of 40K the voltmeter reads. (A) 371 V

(B) 383 V

(C) 394 V

(D) 406 V [GATE-2012, IIT-Delhi]

Q.16 Three moving iron type voltmeter are connected as shown below voltmeters reading are V1 and V2 as indicated. The

correct relation among voltmeter reading is

V

(A) V 

 j1 

j2 

V1

V2

V1 V2  2 2

(C) V  VV 1 2

A Voltmeter +

(B) 3.15 (D) 0 [GATE-2013, IIT-Bombay] Q.18 Two ammeter X and Y have resistances of 1.2  & 1.5  respectively and they give full

+

V i (t )

100 K

(A) 4.46 (C) 2.23

–

10 k

~

I

(B) V  V1  V2 (D) V  V2 V1

[GATE-2013, IIT-Bombay] Q.17 The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite. Assuming that the diode shown in figure below is ideal, reading of the voltmeter in volts is

scale deflection with 150 mA and 250 mA respectively. The ranges have been extended by connecting shunts so as to give full scale deflection with 15 A. The ammeters along with shunts are connected in parallel and then placed in a circuit in which the total current flowing is 15 Amp. The current in ammeter indicated in ammeter X is________. [GATE-2014, IIT-Kharagpur] Q.19 The dc current flowing a circuit is measured by two ammeter, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, the flux density in the air gap is

0.2 Wb/m2 and the area of this coil is 80mm2 . The electrodynamometer ammeter has a change in mutual inductance with respect to deflection of 0.5mH/deg . The spring constant of both the are equal. The value of current, at which the deflection of the two meters are same is________. [GATE-2014, IIT-Kharagpur] Q.20 A 0-1 Ampere moving iron ammeter has an internal resistance of 50 m  and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating frequencies. The time constant in milliseconds and resistance in m  of the shunt coil respectively are (A) 2, 5.55 (B) 2, 1 (C) 2.18, 0.55 (D) 11.1, 2 [GATE-2018, IIT-Guwahati]

GATE ACADEMY®

19

Q.21 Thermocouples measure temperature based on [GATE-2019, IIT-Madras] (A) Photoelectric effect (B) Seebeck effect (C) Hall effect (D) Thermal expansion Q.22 A moving coil instrument having a resistance of 10 , gives a full-scale deflection when the current is 10 mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to 100 V? [GATE-2019, IIT-Madras] (A) 9 (B) 9990

(C) 990

Basic Instruments

(C) Increase the sensitivity (D) Increase the field strength Q.5

(A) Much larger than unity (B) Of the order of unity (C) Much less than unity (D) Made deflection-dependent Q.6

rise in temperature of 100 C , the instrument reading will

(D) 99

Q.2

If one of the control springs of a Permanent Magnet Moving Coil ammeter is broken then, when connected it will read (A) Zero (B) Half of the correct value (C) Twice the correct value (D) an infinite value. The coil of a moving coil ammeter of 100 turns is 40 mm, long and 30 mm wide. The control torque is 240 106 Nm on full

(A) Increase by 0.2% (B) Decrease by 0.2% (C) Increase by 0.6% (D) Decrease by 0.6% Q.7

Q.8

scale. If the magnetic flux density in the air-

Q.3

gap is 1 Wb/m 2 , what will be the range of the ammeter? (A) 1 mA (B) 2 mA (C) 3 mA (D) 4 mA A moving iron instruments has a resistance of 10 ohms and takes 40 mA to produce full. Scale deflection. The shunt resistance required to covert this instrument for use as an ammeter of range 0 to 2 A is (A) 0.1021  (B) 0.2041  (C) 0.2561 

Q.4

(D) 0.4210 

Swamping resistance is a resistance which is added to the moving coil of a meter to (A) Reduce the full-scale current (B) Reduce the temperature error

In a PMMC instrument, the central spring stiffness and the strength of the magnet decrease by 0.04% and 0.02% respectively due to a rise in temperature by 10 C . With a

Practice (objective & Num Ans) Questions :

Q.1

An indicating instrument is more sensitive if its torque to weight ratio is

Q.9

A spring controlled moving iron voltmeter draws a current o 1mA for full scale value of 100V. If it draws a current of 0.5mA, the meter reading is (A) 25V

(B) 50V

(C) 100V

(D) 200V

Torque/weight indicate

ratio

of

an

instrument

(A) Selectivity

(B) Accuracy

(C) Fidelity

(D) Sensitivity

Which one of the following types of instruments can be used to determine the r.m.s. value of ac voltage of high magnitude (10 kV) and of any wave shape? (A) Moving iron instruments (B) Dynamometer type instruments (C) Induction instruments (D) Electrostatic instruments

Q.10 The

current

passing

through

a

10

resistance is given by i  3  4 2 sin 314t this current is measure by a PMMC meter. What is the measured value?

Electrical & Electronic Measurements [Workbook]

(A) 3A

(B) 4A

(C) 5 A

(D) 4 2A

GATE ACADEMY®

20 Q.2

moving-iron ammeter is 6 105 N-m. What is the rate of change of self-inductance with respect to the deflection of the pointer of the ammeter at full scale? (A) 0.5  H/rad (B) 0.2  H/rad

Q.11 A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale deflection. The external shunt resistance (in milliohms) needed to extend its range to (0-500 A) is _________. Q.12 Match the following

(C) 1.3  H/rad Q.3

Instrument Types

P. Permanent magnet moving coil Q. Moving iron connected through current transformer R. Rectifier S. Electrodynamometer Used for

1. DC only 2. AC only

Q.4

3. AC and DC P Q R S

(A) 1 2 1 3 (B) 1 3 1 2 (C) 1 2 3 3 (D) 3 1 2 1 Q.13 A dc voltage with ripple is given by v(t )  [100  10sin(t )  5sin(3t )] volts.

Q.5

(D) 0.3  H/rad

A moving-coil instrument has a resistance of 10  and gives a full-scale deflection when carrying a current of 50 mA. What external resistance should be connected so that the instrument can be used to measure current up to 50 A? (A) 20  in parallel (B) 100  in series (C) 0.010  in parallel (D) 18.7  in series A moving-coil meter has a resistance of 3  and gives full-scale deflection with 30 mA. What external resistance should be added in series so that it can measure voltages up to 300 V? (A) 10  (B) 9997  (C) 0.19  (D) 0.01  A basic D’Arsonval movement showing full scale deflection for a current of 50 A and

Measurement of this voltage v(t ) , made by

having internal resistance of 500 is used

moving-coil and moving-iron voltmeters, show readings of V1 and V2 respectively.

as a voltmeter. What is the value of multiplier resistance needed to measure a voltage range of 0 – 20 V?

The value of V2  V1 , in volts, is ________. Assignment (objective & Num Ans) Questions :

Q.1

The full-scale deflecting torque of a 20 A

For a certain dynamometer ammeter the mutual inductance (M) varies with

Q.6

(A) 398.5k

(B) 399k

(C) 399.5k

(D) 400k

A galvanometer has a current sensitivity of 1μA/mm and critical damping resistance of

deflection 0 as M  6cos(  300 )mH .

1k . The voltage sensitivity and the mega-

Find the deflecting torque produced a direct current of 50 mA corresponding to a

ohm sensitivity respectively are

deflection of 600 .

(B) 1 mV/mm and 22M

(A) 1 mV/mm and 1M

(A) 10 N-m

(B) 20 N-m

(C) 2 mV/mm and 2M

(C) 15 N-m

(D) 1.5 N-m

(D) 2 mV/mm and 1M

GATE ACADEMY®

Q.7

Q.8

21

Basic Instruments

A moving coil instrument of resistance 5

(A)  0.25A

(B)  0.12A

requires a potential difference of 75 mV to give a full scale deflection. The value of shunt resistance needed to give a full scale deflection at 30 A is

(C) 0.37A

(D) 0.5A

(A) 2.5m

(B) 9.99m

(C) 5

(D) 9.95

in 100 V range, the current through the voltmeter is (A) 100 mA (B) 50 mA (C) 1 mA (D) 0.5 mA Q.9 If an ammeter is to be used in place of a voltmeter, we must connect with the ammeter a (A) High resistance in parallel (B) High resistance in series (C) Low resistance in parallel (D) Low resistance in series Q.10 The different torques acting on the coil of a moving coil instrument are (A) Deflecting torque and control torque. (B) Deflecting torque and damping torque. (C) Control torque and damping torque. (D) Deflecting torque, control torque and damping torque. Q.11 A current waveform i(t ) , shown in the

i(t)A

figure, is passed through a Permanent Magnet Moving Coil (PMMC) type ammeter. The reading of the ammeter up to two decimal places is 2 1.5 1 0.5 0

0

1

2

3 4 t (ms)

5

6

(A) Dynamometer-type ammeter (B) Dynamometer-type wattmeter (C) Moving-iron voltmeter

A dc voltmeter has a sensitivity of 1000Ω/V . When it measures half full scale

– 0.5 –1 – 1.5 –2

Q.12 Identify the instrument that does not exist :

7

(D) Moving-iron wattmeter Q.13 When the voltage across a battery is measured using a dc potentiometer, the reading shows 1.08 V. But when the same voltage is measured using a permanent magnet moving coil (PMMC) voltmeter, the voltmeter reading shows 0.99 V. If the resistance of the voltmeter is 1100 , the

internal resistance of the battery, in  is _______.

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

22

Answer Keys

Objective & Numerical Answer Type Questions 1.

85

2.

57.7

3.

150

4.

D

5.

C

6.

C

7.

A

8.

A

9.

C

10.

C

11.

C

12.

C

13.

A

14.

C

15.

D

16.

B

17.

A

18.

10.14

19.

3.2

20.

A

21.

B

22.

B

Practice (Objective & Numerical Answer) Questions 1.

A

2.

B

3.

B

4.

B

5.

A

6.

A

7.

A

8.

D

9.

D

10.

A

11.

0.22

12.

C

13.

0.312

Assignment (Objective & Numerical Answer) Questions 1.

C

2.

D

3.

C

4.

B

5.

C

6.

A

7.

A

8.

D

9.

B

10.

D

11.

A

12.

D

13.

100 

3

Measurement of Power

Formulas & Logics 3.1

Measurement of AC Power : 3.1.1 Electrodynamometer type wattmeter : Dynamometer type wattmeter consists of two coils called moving coil and fixed coil. Moving coil is connected parallel to the load and it is also called pressure coil, the pressure coil is made up of thin conductors. So, that torque to weight ratio is high, and hence the sensitivity. It is designed to carry small current.

I2 (DPST)

F.C.1

F.C.2

I2

I1

I1 I1

1  Supply

I2

( I1  I 2 )

I1

L (Lag O Power A D Factor)

Fig. Circuit diagram of electrodynamometer type wattmeter A potential coil of wattmeter must be highly resistive so that errors in the measurement of power is minimized. M

L M : Supply mains L : Load

C

C : Common point V : Voltage V

Fig. Symbol of electrodynamometer wattmeter

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

24

Spring control is used. Air friction damping is used. Torque equation : For electrodynamometer type instruments : dM Td avg  I1I 2 cos  d Potential coils is highly resistive so, IV dM V Td avg  1 cos  I2   Rs Rs d

Pavg dM Rs d 

Td avg  3.2



Td avg  Pavg

Therefore, wattmeter gives average output active power. Harmonic Signal : PC Circuit is energized by instantaneous voltage, v  V0  V1 sin(t  1 )  V2 sin(2t  2 )  ......... CC Circuit is energized by instantaneous current, i  I 0  I1 sin(t  1 )  I 2 sin(2t  2 )  .........



Pavg 

1 2

2

 vi d (t ) 0

Wattmeter reading : 1 Pavg  V0 I 0  V1I1 cos(1  1 )  V2 I 2 cos(2  2 )  ......... 2 where, V1 ,V2 .............I1 , I 2 ............. are peak values 3.3

3.4

Blondel’s Theorem : For measurement of total power in a “N” phase system, the number of wattmeters required are “N-1”. Measurement of 3 Power using 2 Wattmeter Method : (i) Star load (ii) Delta load (i) For star load : W2

IR

R

ZÐf

VRB

N

W1 B

ZÐf

IB

VRY VBY Y

IY

Fig. Circuit diagram

ZÐf

GATE ACADEMY®

25

Measurement of Power

VBY IB

VY

(30 0 – f)

V

BN

VRY

0

30

300

(300 + f)

f

VRN IR

VYN

Fig. Phasor diagram Wattmeter reads, W1  VBY I B cos(300  )  VL I L cos(300  )

…(i)

W2  VRY I R cos(300  )  VL I L cos(300  )

…(ii)

Total power, Ptotal  W1  W2

Ptotal  3VL I L cos  (ii) Delta load : W2

IR

R

R

I BR

I RY

VRB W1

VRY

IB

B

B

IYB

VBY IY

Y

Fig. Circuit diagram IBR IB IBR

0

30

–

f

VBY

300

IYB

VYB

300

f VRY

f IRY 30 0 +f IR

Fig. Phase diagram

Y

GATE ACADEMY®

26

Electrical & Electronic Measurements [Workbook]

Wattmeter reads,

W1  VBY I B cos(VBY ~ I B )  VL I L cos(300  ) W2  VRY IY cos(VRY ~ IY )  VL I L cos(300  ) Total power,

P  W1  W2  VL I L [cos(300  )  cos(300  )]

 3VL I L cos  Total 3-  reactive power, W1  W2  VL I L [cos(300  )  cos(300  )]

W1  W2  VL I L sin 

3(W1  W2 )  3 VL I L sin  3.5

Measurement of Reactive Power : If the wattmeter current coil is connected to one of the phase i.e. Y and the potential coils is connected between the remaining two phase then wattmeter reads reactive power. M

L W1

C

V

Fig. Circuit diagram VBN

IB f f f

IY VYN

300

60 300 90 - f

0

VRN IR -VBN

VYB

Fig. Phasor diagram

GATE ACADEMY®

27

Measurement of Power

Wattmeter reading, W1  VYB I R cos(900  )

W1  VL I L sin 

W1  Reactive power

Total 3-  Reactive power  3W1 3.6

Measurement of Power Factor Angle : Total active power, W1  W2  3VL I L cos 

Total reactive power,

…(i)

3(W1  W2 )  3VL I L sin 

…(ii)

From equation (i) and (ii),

3(W1  W2 ) sin   W1  W2 cos 

 W  W2  tan   3  1   W1  W2  3.6.1 Effect of load power on wattmeter reading :  W1  VL I L cos (30  ) W2  VL I L cos (30  ) W1  W2

450

3 VL I L 2 VL I L 2 0.25VL I L

600

0

900

 VL I L 2

0 300

3.7

3 VL I L 2

…(iii)

3 VL I L

3 VL I L 2 1.21VL I L

VL I L 0.926VL I L 3 VL I L 2 VL I L 2

3 VL I L 2

0

If one of the wattmeter indicated negative value change either (C.C) or (P.C) Terminals but not both and record reading with negative sign. If one of the wattmeter indicated negative value then the power factor of the load is less than 0.5 value. Errors in Wattmeter 3.7.1 Error due to connection of potential coil : Where, rc  Current coil resistance

PT  True power of load  (V I L cos )

IC » I L

PL  Power loss in C.C = I L2 rc

rc

Pm  Measured power Pm  PT  I L rc 2

I 2r P P % Error = m T  100% = L c 100% PT PT

V

IL

P.C Rs

L O A D

GATE ACADEMY®

28

Electrical & Electronic Measurements [Workbook]

3.7.2 Error due to potential coil inductance : C.C

I1 = I L I2

I2

V

f

L O A D

P.C Rs

V

I1

Fig. Circuit diagram

Fig. Phasor diagram C.C I LP

V

I2

RP

Load

Rs

Fig. Circuit diagram

P.C.

Fig. Potential coil with inductance Z P  ( RP  Rs )  jLP

Assume, RP  Rs Then, Z P  Rs  jLP wLP

ZP b

Rs

Fig. Potential coil cos  

Rs ZP

…(i)

Where   Impedance angle V

b f f-b

I2

I1 Fig. Phasor diagram with pressure coil inductance

GATE ACADEMY®

29

Td  I1I 2 cos(  )

Td 

dM V dM I cos(  ) d ZP d

V I cos  dM cos(  ) Rs d

Td  V I cos  cos(  ) Pm  V I cos  cos(  ) Error :

PM  PT  100% PT

cos  PT cos    2 PM cos [cos  cos   sin  sin ] cos  cos (1  tan  tan )



1  tan 2  sec 2   1  tan  tan  1  tan  tan 

If  is small then 1  tan 2   1

PM  1  tan  tan  PT

Then, Error :

PM  PT  tan  tan  PT

%Error 

PM  PT 100%  tan  tan  PT

Measurement of Power

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

30

(A) The active power in the load is 1.732 KW (B) The reactive power of the load is 1.732 KVAr (C) The active power in the load is 3 KW (D) The reactive power of the load is 3 KVAr [GATE-2004, IIT-Delhi] A sampling wattmeter (that computes power from simultaneously sampled values of current and voltage) is used to measure an average power of a load. The peak to peak voltage of the square wave is 10 V and the current is a triangular wave 5A P - P as shown in figure. The period is 20 ms. The reading of wattmeter will be,

Objective & Numerical Ans Type Questions :

Q.1

VRN , VYN and VBN are the instantaneous line to neutral voltages and iR , iY and iB are the instantaneous line currents in a balanced three-phase circuit, the computation, VRN (iY  iB )  (VYN  VBN ) iR will yield a

Q.2

quantity proportional to (A) The active power (B) The power factor (C) The reactive power (D) The complex power [GATE-1993, IIT-Bombay] The line to line voltage to the 3-phase 50 Hz ac circuit as shown in figure is 100 V arm. Assuming that the phase sequence is RYB the wattmeter would read.

Q.4

W1

R

0

5Ð60

5Ð600

0

5Ð600

0

Y

(A) 0 W (C) 50 W

B

W2

(A) W1  886 Watt, W2  896 Watt

Q.5

(B) W1  500 Watt, W2  500 Watt (C) W1  0 Watt, W2  1000 Watt (D) W1  250 Watt, W2  750 Watt

W

R M Y com

B

V

Balance R-L load

Balance symmetrical source

Q.3

[GATE-2002, IISc-Bangalore] A 3-phase balanced R-L load is connected to a 3-phase balanced symmetrical 400 V, 50 Hz, RYB sequence mains as shown in figure. The wattmeter W reads 1.732 KW. Then

(B) 25 W (D) 100 W [GATE-2006, IIT-Kharagpur] The figure shows a three-phase delta connected load supplied from a 400 V, 50 Hz, 3-  balance source. The pressure coil (PC) and current coil (CC) of a wattmeter are connected to the load as shown, with the coil polarities suitably selected to ensure a positive deflection. The wattmeter reading will be, R

3f

Z1

Supply 400 V 50 Hz

Z2 CC

Y B

Z1  100 , Z2  100 

PC

GATE ACADEMY®

31

Measurement of Power

(A) 0

(B) 1600 Watt

carries a current of

(C) 800 Watt

(D) 400 Watt

voltage across pressure coil is

[GATE-2009, IIT-Roorkee] Q.6

If the switch is moved to position Y, the readings of the watt-meters in watts will be, W1 R

2 sin(100t )

V. The meter will indicate

The load shown in the figure is supplied by a 400 V (line-to-line), 3-  source (RYB sequence). The load is balanced and inductive, drawing 3464 VA. When the switch S is in position N, the three wattmeters W1 , W2 and W3 read 577.35 W each.

2 cos(100t ) A. The

(A) 0 W

(B) 100 W

(C) 200 W

(D) 400W [GATE-2003, IIT-Madras]

Q.9

A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The power consumed by the load is 5 kW. The power is measured by the twowattmeter method. The readings of the two wattmeters are (B) 2.50 kW and 2.50 kW

Y

LOAD

400V,3-phase source

(A) 3.94 kW and 1.06 kW W2

W3 B S

(C) 5.00 kW and 0.00 kW (D) 2.96 kW and 2.04 kW

Y

[GATE-2015, IIT-Kanpur]

N

Q.10 The coils of a wattmeter have resistance 0.01 Ω and 1000 Ω; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The percentage error on the wattmeter reading is _______.

N

(A) W1  1732 and W2  W3  0 (B) W1  0, W2  1732 and W3  0 (C) W1  866, W2  0, W3  866 (D) W1  W2  0 and W3  1732 [GATE-2017, IIT-Roorkee] Q.7

A 5 A, 110 V electrodynamic type wattmeter has a scale having 110 division. Its pressure coil is fed by a voltage of 110 2 cos(314t )  2 sin(942t )  V and its   current coil carrying a current of 5 2 cos(314t  60)  2 2 sin(628t  90)   A.  2 cos(642t  90)  

The needle of wattmeter will move to

[GATE-2015, IIT-Kanpur] Q.11 The voltage (V) and current (A) across a load are as follows.

(A) 110 divisions

(B) 50 divisions

v(t )  100sin (t )

(C) 54 divisions

(D) 55 divisions

i(t )  10sin(t  600 )  2sin(3t )  5sin(5t ) .

[GATE-2002, IISc-Bangalore] Q.8

Load

The current coil of a 200 V, 5 A electrodynamometer type LPF wattmeter

The average power consumed by the load, in W, is ________. [GATE-2016, IISc-Bangalore]

GATE ACADEMY®

32

Practice (objective & Num Ans) Questions :

Q.2

Q.3

Q.4

Q.5

Q.6

The resistances of two coils of a wattmeter are 0.01 ohm and 1000 ohms respectively and both are non-inductive. The load current is 20A and the voltage across the toad is 30V. In one of the two way of connecting the voltage coil, the error in the reading would be (A) 0.1% too high (B) 0.2% too high (C) 0.15% too high (D) Zero Two-wattmeter method is employed to measure power in a 3-phase balanced system with the current coils connected in the A and C lines. The phase sequence is ABC. If the wattmeter with its current coil in A-phase line reads zero, then the power factor of the 3-phase load will be (A) Zero lagging (B) Zero leading (C) 0.5 lagging (D) 0.5 leading The ratio of the readings of two wattemeters connected to measure power in a balanced 3- phase load is 5 : 3 and the load is inductive. The power factor of load is (A) 0.917 lead (B) 0.917 lag (C) 0.6 lead (D) 0.6 lag In a two-wattmeter method of measuring power, one of the wattmeter is reading zero watts. The power factor of the circuit is (A) Zero (B) 1 (C) 0.5 (D) 0.8 If the readings of the two wattmeters are equal and positive in two wattmeter method, the load pf in a balanced 3-phase 3-wire circuit will be (A) Zero (B) 0.5 (C) 0.866 (D) Unity In the circuit shown in the given figure, the wattmeter reading will be

200 V 1-f supply

(4 + j 3) W

50/5 A

CT

M

Q.7

Q.8

L

(A) 480 W (B) 640 W (C) 800 W (D) 1000 W In the measurement of power on balanced load by two-Wattmeter method in a 3-phase circuit, the readings of the Wattmeters are 3 kw and 1 kW respectively, the latter being obtained after reversing the connections of the current coil. The power factor of the load is (A) 0.277 (B) 0.554 (C) 0.625 (D) 0.866 Two types of connections of Wattmeter pressure coil are shown in the figures. The value of the Wattmeter current coil resistance r, which makes the connection errors the same in the two cases is 20 A

V

10 kW

20 A

10 kW

Type 1

(A) 0.05 Q.9

V

Load

Q.1

Load

Electrical & Electronic Measurements [Workbook]

V = 200 V

Type 2

(B) 0.1

(C) 0.01 (D) 0.125 A capacitor is connected across a portion of resistance of the multiplier in order to make the pressure coil circuit of the wattmeter non-inductive. The value of this resistance is r while the total resistance and inductance of the pressure circuit are respectively Rp and L. The value of the capacitance C is 0.41L L (A) 2 (B) r2 RP (C)

L r2

(D)

0.41L RP2

GATE ACADEMY®

33

Q.10 In two-wattmeter method of measuring power in a balanced 3-phase circuit, the readings of the two wattmeters are in the ratio 1 : 2, the circuit power factor is 1 1 (A) (B) 2 2

Measurement of Power Assignment (objective & Num Ans) Questions :

Q.1

3 (D) 1 2 Q.11 Find the wattmeter reading for the following circuit.

(C)

W

I 3W

V = 200 V

250 V 10 kW

Q.2

j4 W

Q.12 Find the wattmeter reading for the following circuit. W

Q.3

I 3W

V = 200 V

(0 – 250 V) 10 kW

j4 W

100Ð250 V

Q.13 Find the wattmeter reading for the following circuit. W

Q.4

I

In an electrodynamometer wattmeter (A) The fixed coils providing magnetic flux are connected across the power line. (B) The compensated wattmeter improves its accuracy by using windings with opposite currents with respect to series windings. (C) If the full-scale power measured is 100 W, then the half-scale power will be 10 W. (D) It can measure a.c. power but is unsuitable for d.c. power. In a two-wattmeter method of measuring power in a balanced 3-phase circuit, the ratio of the two wattmeter readings is 1 : 2. The circuit power factor is (A) 0.707 (B) 0.5 (C) 0.866 (D) Indeterminate A balanced delta-connected load (16  j12)  / phase is connected to a 3phase 230 V balanced supply. The line current and the real power drawn respectively are (A) 19.9 A and 3.17 kW (B) 11.5 A and 6.34 kW (C) 19.9 A and 6.34 kW (D) 11.5 A and 3.17 kW If the total powers consumed by three identical phase loads connected in delta and star configurations are W1 and W2 respectively, then W1 is

3W

W2 3 W (D) 2 (C) 3W2 3 A wattmeter reads 10 kW, when its currents coil is connected in R phase and the potential coil is connected across R and neutral of a balanced 400 V (RYB sequence) supply. The line current is 54 A. If the potential coil reconnected across B-Y phases with the current coil in R phase, the new reading of the wattmeter will be nearly (A) 3W2

V = 200 V j4 W

Q.14 Find the wattmeter reading for the following circuit. W

I 3W

V = 200 V j4 W

Q.5

(B)

Electrical & Electronic Measurements [Workbook]

Q.6

(A) 10 kW

(B) 13 kW

(C) 16 kW

(D) 19 kW

GATE ACADEMY®

34

Q.10 Find the wattmeter reading for the following circuit.

A 400 V, three phase, rated frequency balanced source is supplying power to a balanced three phase load carrying a line current of 5 A at an angle of 30 lagging. The readings of the two wattmeters W1 and

3W

200 V j4 W

IP

C.T

W2 , used for measuring the power drawn by

W

the circuit, are respectively P.T

(A) 2000 W and 1000 W (B) 1500 W and 1500 W

(0 – 300) V 11 kV

(C) 2000 W and 1500 W (D) 1500 W and 1000 W Q.7

consider the following statements with regard to induction type wattmeter. 1. Can be used on both ac and dc systems. 2. Power consumption is relatively low. 3. It is accurate only at stated frequency and temperature. Which of the above statements is/are correct?

Q.8

(A) 1 only

(B) 2 only

(C) 3 only

(D) 1, 2 and 3

For the given voltage and current, the average active power will be ________ kW. v P.C.

200 50 0

C.C.

Q.9

v

300

wt

If instantaneous voltage and current is given by

v  10  5sin(t  450 ) V i  5  3sin (t  150 )  2sin(2t  600 ) A Then find the average active power.

110 kV

(50 A / 5 A) IS

GATE ACADEMY®

35

Measurement of Power

Answer Keys

Objective & Numerical Answer Type Questions 1.

C

2.

C

3.

D

4.

A

5.

B

6.

D

7.

D

8.

A

9.

A

10.

0.15

11.

250 Practice (Objective & Numerical Answer) Questions

1.

C

2.

C

3.

B

4.

C

5.

D

6.

B

7.

A

8.

C

9.

B

10.

C

11.

4.8 kW

1.

B

2.

C

3.

C

4.

A

5.

B

6.

A

7.

C

8.

4.33 kW

9.

56.49 W

10.

264 W

822.76 13. 14. 0W 4.8 W W Assignment (Objective & Numerical Answer) Questions 12.



4

Measurement of Energy & Power Factor

Formulas & Logics Energy meter constant, Number of revolutions made by disc N  (K )  Pt Energy recorded in KWhr Measured energy, Total number of revolution (Wm )  K True energy, VI cos  t (WT )   KWhr 1000 3600 where V  voltage, I = current Measured energy  True energy % Error ( r )   100% True energy

 r  + ve means meter is running fast,  r   ve means meter is running slow. Objective & Numerical Ans Type Questions :

Q.1

If an energy meter disc makes 10 revolutions in 100 seconds when a load of 450 W is connected to it, the meter constant (in rev/kWh) is (A) 1000

(B) 500

(C) 1600

(D) 800 [GATE-2001, IIT-Kanpur]

Q.2

(B) Continue to work, but registers a lower kWhr.

The brake magnet of an error free electromechanical induction type energy meter is shifted from its position and moved a small distance towards the edge of disc. Then the meter will (A) Continue to work correctly without any change in its characteristic.

(C) Continue to work, but registers a higher kWhr. (D) Stop working [GATE-2004, IIT-Delhi] Q.3

A dc A - h meter is rated for 15 A, 250 V. the meter constant is 14.4 A-sec/rev . The meter constant at rated voltage may be expressed as (A) 3750 rev/KWh

(B) 3600 rev/KWh

(C) 1000 rev/KWh

(D) 960 rev/KWh

[GATE-2001, IIT-Kanpur]

GATE ACADEMY®

Q.4

Q.5

A 230 V, 5 A, 50 Hz single phase service energy meter has a meter constant of 360 rev/kWhr. The meter takes 50s for making 51 revolutions of the disc when connected to a 10 kW, unity power factor load. The error in the reading of the meter is (A) 0% (B) + 0.5% (C) – 2.0% (D + 2.0% [GATE-2008, IISc-Bangalore] An energy meter, having meter constant of 1200 revolutions/kWh, makes 20 revolutions in 30 seconds for a constant load. The load, in kW, is ___________. [GATE-2016, IISc-Bangalore]

37

Measurement of Energy & Power Factor

Q.6

Q.2

Q.3

Q.4

Q.5

The meter constant of a single-phase 240V induction watt-hour meter is 400 revolutions per kWh. The speed of the meter disc for a current of 10 ampere at 0.8 p.f. lagging will be (A) 12.8 rpm (B) 16.02 rpm (C) 18.2 rpm (D) 21.1 rpm The phenomenon of creeping occurs in (A) Energy meters (B) Ammeters (C) Wattmeters (D) Voltmeters A single-phase energy meter is operating on 230V, 50Hz supply with a load of 20A for two hours at upf. The meter makes 1380 revolutions in that period. The meter constant is (A) 695 rev/kWh (B) 150 rev/kWh (C) 0.15 rev/kWh (D) 1/150 rev/kWh A 230 V, 10 A, single-phase energy meter makes 90 revolution in 3 minutes at half load rated voltage and unity p.f. If the meter constant is 1800 revolutions/kWh, then its error at half load will be (A) 13.04% slow (B) 13.04% fast (C) 15% slow (D) 15% fast The disc of a house service energy meter of 230V, 1- , 50Hz, 5A, 2400 rev. per kWh creeps at 1 rev. per min. The creep error (in percent) of full load unity pf is

60 100 2400

(B) 

60 100 2400

(C) 

60 100 1.15  2400

(D) 

60 100 1.15  2400

In a single-phase induction type energy meter, the lag adjustment is done to ensure that (A) Current coil flux lags the applied voltage by 900

Practice (objective & Num Ans) Questions :

Q.1

(A) 

(B) Pressure coil flux lags the applied voltage by 900 (C) Pressure coil flux is in phase with the applied voltage (D) Current coil flux lags the pressure coil flux by 900 Assignment (objective & Num Ans) Questions :

Q.1

Q.2

Q.3

An energy meter having a meter constant of 1200 rev per kWh is found to make 5 revolution in 75s. The load power is (A) 500 W

(B) 100 W

(C) 200 W

(D) 1000 W

A single-phase energy meter having meter constant of 200 rev/kWh is operating on 230V, 50Hz supply with a load of 10A and at unity power factor for three hours continuously. The number of revolutions shown by the meter during this period is (A) 13800

(B) 1380

(C) 276

(D) 138

The meter constant of a single-phase energy meter is 500 rev/kWh. It is found that with a load of 5kW, it makes 40 revolutions in 50 sec. The percentage error is (A) 5.25%

(B) 10.5%

(C) 15.25%

(D) 20%

Electrical & Electronic Measurements [Workbook]

Q.4

GATE ACADEMY®

38

One single-phase energy meter operating on 230 V and 5 A for 5 hours makes 1940 revolutions. Meter constant is 400 rev/kWh. The power factor of the load is

Q.5

(A) 1.0

(B) 0.8

(C) 0.7

(D) 0.6

The meter constant of a single phase 230 V induction watt hour meter is 400 revolutions per kWh. The speed of the meter disc for a current of 10 A of 0.9 pf lagging will be

Q.6

(A) 13.80 rpm

(B) 16.02 rpm

(C) 18.20 rpm

(D) 21.10 rpm

If an energy meter makes 5 revolutions in 100 seconds, when a load of 225 W is connected, the meter constant is (A) 800 rev/kWh

(B) 222 rev/kWh

(C) 147 rev/kWh

(D) 13 rev/kWh

Answer Keys

Objective & Numerical Answer Type Questions 1.

D

2.

B

3.

C

4.

D

5.

2

5.

C

5.

A

Practice (Objective & Numerical Answer) Questions 1.

A

6.

B

2.

A

3.

B

4.

A

Assignment (Objective & Numerical Answer) Questions 1.

C

6.

A

2.

B

3.

C

4.

C



5

Measurement of Resistance

Formulas & Logics 5.1

Medium Resistance Measurement Methods : A Q Ig

B

V

I1 I 2

S

C

G

P

R D

Fig. Circuit diagram

Rth = Ig 

SR PQ + PQ RS

…(iii)

Vth V [ PS  QR]  Rth  Rg ( P  Q)( R  S )( Rth  Rg )

When bridge is balanced i.e. I g = 0 PS – QR = 0



R=

PS Q

…(iv)

5.1.1 Current sensitivity : S1 

 mm/μA Ig

5.1.2 Voltage sensitivity :

SV 

 mm/v Vth

5.1.3 Bridge sensitivity :

SB 

θ mm R / R

(   Deflection of galvanometer is in mm)

5.2

GATE ACADEMY®

40

Electrical & Electronic Measurements [Workbook]

Condition for Maximum Bridge Sensitivity Under Balanced Condition : Q

S G

B

V

T20 C

C Ig ¹ 0

R + DR

P

T10 C

Boiler

5.3

Fig. Variation of unknown resistance R P Condition for maximum S B ,  1 S Q Then equation (ii) become V  SV S B max  4 Substitution Method : A Switch

Rg

G

Rh

B I

S

V

5.4

Fig. Circuit diagram RT  S Low Resistance Measurement Method : 1. Kelvin double bridge 2. Potentiometer method 3. V-I method Kelvin Double Bridge : B

P

Q

G

E p

A

D R Test resistance

q

r lead resistance

S Standard resistance

M V

RT

Fig. Circuit diagram

C

…(iii)

GATE ACADEMY®

41

Measurement of Resistance

where, P, Q  Outer arms resistance. p, q  Inner arms resistance

S  Standard resistance

R

PS qr  P P    Q p  q  r  Q q 

If

P p  Q q

then

R

5.5

P S Q

Measurement of High Resistance 1. Meggar. 2. Direction Deflection method. 3. Loss of charge. Direction deflection method : A I

V

V

Cable

Fig. Circuit diagram High voltage is applied across specimen. Then some μ A current flows though it which is read by galvanometer. Ratio of voltmeter to Ammeter gives resistance of specimen i.e. R  Loss of charge method : Switch V

V VC

C

Fig. Circuit diagram R

0.4343 t V  C log    VC 

R (Test)

V . I

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

42

(A) 2.255% (C) 4.5%

Objective & Numerical Ans Type Questions :

Q.1

Kelvin double bridge is best suited for the measurements of (A) Inductance

(B) Capacitance

(C) Low resistance

(D) High resistance

Q.5

[GATE-1995, IIT-Kanpur] Q.2

In the context of low resistances, identify the incorrect statement (A) Standard low resistance have four terminal construction. (B) Kelvin bridge is used for measuring low resistance, precision depends up on detector sensitivity.

Q.6

in ms (round off to two decimal places) required for the voltage across the capacitor to drop to 1 V is _______. [GATE-2019, IIT-Madras] Practice (objective & Num Ans) Questions :

Q.1

[GATE-2001, IIT-Kanpur] Q.3

Kelvin double bridge is best suited for the measurement of (A) Resistance of very low value

A resistor R is measured using the V-I method, with V read as 10.14V and I as 5.07mA. Which one of the following expresses the value of resistance? (A) 2 k (B) 2.00 k (C) 2000 

Q.2

(B) Low value of capacitance (C) Resistance of very high value (D) High value capacitance

In the circuit shown below, the ammeter reads 0.1 A and the voltmeter reads 10 V. The internal resistance of the ammeter is 1  and that of the voltmeter is 500  . A

The setup in the figure is used to measure resistance R. The ammeter and voltmeter resistance are 0.01 and 2000 

V

respectively. Their readings are 2 A and 180 V respectively, giving a measured resistance of 90 . The percentage error in the measurement is

RL

V

Q.3 A

(D) 2.0 k

What is the value of R?

[GATE-2002, IISc-Bangalore] Q.4

(A) Wien’s bridge (B) Kelvin double bridge (C) Maxwell’s bridge (D) Schering bridge [GATE-2015, IIT-Kanpur] A 0.1F capacitor charged to 100 V is discharged through a 1 k resistor. The time

(C) A pair of ratio arms in Kelvin double bridge for measuring the low resistance eliminates the error due to thermo emf. (D) Low resistances use for ammeter shunts are usually made with a suitable number of plates of large area and all the plates connected in parallel.

(B) 2.35% (D) 4.71% [GATE-2005, IIT-Bombay] The bridge most suited for measurement of a four-terminal resistance in the range of 0.001 to 0.1 is

R

(A) 100 

(B) 125 

(C) 90 

(D) 120 

In measuring resistance by voltmeterammeter method, the voltmeter can be connected either across supply or across the resistance. If the resistance is low, the voltmeter should be connected

GATE ACADEMY®

43

(A) Across the supply. (B) Across the resistance. (C) Either across the supply or across the resistance. (D) Neither across the supply nor across the resistance.

Measurement of Resistance

Q.3

(B) – 5%

(C) 2%

(D) 5%

Which one of the following methods is used for the measurement of high resistances? (A) Carey-Foster bridge method (B) Substitution method

Assignment (objective & Num Ans) Questions :

(C) Loss of charge method

A megger is an instrument used for measuring

Q.1

(A) – 2%

(D) Potentiometer method Q.4

(A) Very high voltages (B) Very low voltages

Calculate insulation resistance of a cable in which the voltage falls form 100 V to 80 V in 20 sec. The capacitance is 300 pF.

(C) Very high resistances (D) Very low resistances The values of ammeter and voltmeter resistances are 0.1  and 2000  respectively as shown in the figure below. The percentage error in the calculated value of R = 100  (voltmeter reading 200 V/ammeter reading 2 A) is nearly

Q.2

R

A RA = 0.1 W

V RV = 2000 W

Answer Keys

Objective & Numerical Answer Type Questions 1.

C

6.

0.46

2.

C

3.

A

4.

D

5.

B

Practice (Objective & Numerical Answer) Questions 1.

C

2.

B

3.

A

Assignment (Objective & Numerical Answer) Questions 1.

C

2.

B

3.

C

4.

2.987  1011  

6

Potentiometer

Formulas & Logics VB

Rh l2

l1 l

C

D

E

(sliding wire)

Ig

Vx B VS

Iw

(sliding contact)

G

Test cell A

Switch

Standard cell

Fig. Circuit diagram Vx 

Vs l2 l1

where, r  resistance of slide wire ( Ω/m ),

l  total length of slide wire (m), l1  length at which standard cell is balanced, l2  length at which test voltage Vx is balanced.

6.1

Resolution of Potentiometer : Resolution is smallest value which can be measured or read from scale. Resolution is smallest value of reading for given range which be measured accurately. R

V V  l mm

R

Full scale value Number of steps

GATE ACADEMY®

45

Objective & Numerical Ans Type Questions :

Q.5

In the potentiometer circuit shown in the figure, the expression for Vx is

A dc Potentiometer is designed to measure up to 2V with a slide wire of 800 mm. A standard cell of emf 1.18 V obtains balance at 600 mm. A test cell is seen to obtain balance at 680 mm. The emf of test cell is [GATE-1994, IIT-Khragpur] (A) 1.00 V (B) 1.34 V (C) 1.50 V (D) 1.70 V In the Potentiometer circuit shown in figure balance is obtained. The unknown E x is

Q.2

then

[GATE-1994, IIT-Kharagpur] 200 W

3.2

[GATE-2015, IIT-Kanpur]

V

V

R aR

+

Q.1

Potentiometer

Vx

(A) (1  2 )V

(B) (1  )V

(D) V (C) (  1)V A dc potentiometer, shown in figure below, is made by connecting fifteen 10  resistors

Q.6

and a 10  slide wire of length 1000 mm in 200 W

series. The potentiometer is standardized with the current I p  10.0000 mA. Balance

2800 W

for an unknown voltage is obtained when the dial is in position 11 (11numbers of the fixed 10  resistors are included) and the slide wire is on the 234th mm position. The unknown voltage (up to four decimal places) in volt is ______. [GATE-2016, IIT-Kanpur]

200 W

Ex

Rg = 100 W

(A) 200 mV (B) 2.8 V (C) 3.0 V (D) 400 mV A resistance Potentiometer has a total resistance of 10000  and is rated 4 W. If the range of the Potentiometer is 0 to 100 mm then its sensitivity is V/mm. [GATE-1999, IIT-Bombay] (A) 1.0 (B) 2.0 (C) 2.5 (D) 25 The wiper of the 20 k Potentiometer in the figure is Positioned half way. Then the voltage V0 of the circuit is

Q.3

Q.4

[GATE-1999, IIT-Bombay]

RC

RF

VB

234 mm

IP 0 mm 16

15

14

13

12

11

10

9

8

7

6

20 KW

-

RH

200 cm V0

100 cm

+

(B) – 1.0 V (D) 2.5 V

1

0

Common Data Question For Q.1 and Q.2 A slide wire potentiometer AB is shown in figure. It has a resistance of 1 Ω/cm . A voltage of E  1V is

A

(A) – 1.5 V (C) – 0.75 V

2

Practice (objective & Num Ans) Questions :

-

10 KW

3

VX

4V 2V +

4

G

balanced against 100 cm.

15 KW

5

1000 mm

B

E

G

RH = 50 W

Electrical & Electronic Measurements [Workbook]

Q.1

Calculate the potentiometer current and resistance of rheostat RH .

Q.2

Calculate the current that would flow through the galvanometer if the terminals of battery get reversed accidentally. A simple dc potentiometer is to be standardized by keeping the slide wire setting at 1.0183V. If by mistake, the setting is at 1.0138V and the standardization is made to obtain a source voltage of 0.0138V, then the reading of the potentiometer will be (A) 1.0138 V (B) 1.0183 V

Q.3

GATE ACADEMY®

46

Q.2

magnitude of the current, if the standard cell having an emf of 1.45 volts is balanced at 50 cm? (A) 3.09 A (B) 2.65 A (C) 2.03 A (D) 1.45 A A RC potentiometer to measure ac voltage, V it is desired that 0 should be independent V1 of frequency. The value of C should be

R1

10 K

C1

2

(1.0138) (D) (1.0138) 2 V V 1.0183 A slide wire potentiometer has 10 wires of l m each. With the help of a standard voltage source of 1.018V it is standardized by keeping the jockey at 101.8cm. If the resistance of the potentiometer wires is 1000 ohm, then the value of the working current is (A) 0.1 mA (B) 0.5 mA (C) 1 mA (D) 10 mA

(C) Q.4

R2

Q.3

Assignment (objective & Num Ans) Questions :

Q.1

1mF

V1 1K

C

V0

(A) 10 F

(B) 11F

(C) 0.1F

(D) 0.09 F

What is the number of turns of wire needed to provide a potentiometer with a resolution of 0.05 percent? (A) 200 turns (B) 2000 turns (C) 20 turns (D) 20000 turns

A single slide wire is used for the measurement of current in a circuit. The voltage drop across a standard resistance of 1.0  is balanced at 70cm. What is the

Answer Keys

Objective & Numerical Answer Type Questions 1.

B

6.

1.1234

2.

A

3.

B

4.

A

5.

A

Practice (Objective & Numerical Answer) Questions 1.

10 mA, 200 

2.

16 mA

3.

C

4.

D

Assignment (Objective & Numerical Answer) Questions 1.

C

2.

A

3.

B

4. 

Instrument Transformer

7

Formulas & Logics 1. Equivalent circuit of C.T. : rP

VP

jxP

Ip

nI s

rS

rl

Im

Iw

ES

EP

jX0

R0

jxS

IS

VS jxl

N1 : N 2

Fig. Equivalent circuit diagram of C.T. Turns ratio :

n

Nominal ratio : K  R

IP Primary winding current  I S secondary winding current IP Rated primary winding current  I S Rated secondary winding current B

EP

90 – (d + a) d a

A

C IP

S

Actual ratio :

N2 Number of turns of secondary winding  Number of turns of Primary winding N1

nI

where,

Iw

q I0

d 0

a Im

d

IS

ES

Fig. Phasor Diagram

f

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

48

 X  XS    tan 1  L   RL  RS   I cos   I  sin  I sin  cos   I 0 cos  sin  I  n  R  P  n  0 IS IS IS

where,

2. Errors in current transformer (CT) : 2.1 Ratio Error :

The turns ratio of the CT is not equal to the current ratio i.e.

IP , but due to the no load component IS

of current ( I0 ) error occurs called ratio error. % 

K R  100% R

 I P N2 I where, K  nominal ratio    n , R  Actual ratio  P I S N1 IS

2.2 Phase angle error :

In ideal transformer primary to secondary current has a phase angle of 1800 but in practical current transformer, due to no load component ( I0 ) error occurs in the phase angle called phase angle error. 

I 0 cos(   ) I 0 cos  cos   I 0 sin  sin   rad nI S nI S



I  cos   I  sin  1800   nI S

For purely resistive load   0 , I  1800    nI S 3. Potential Transformer rP

VP

jxP

Ip

I s /n Im

Iw

R0

jX0

rS

IS

rl ES

EP

VS jxl

N1 : N 2

where

jxS

Fig. Equivalent circuit diagram of P.T N Turns ratio: n  1 N2  VP Actual ratio: R   VS  VP Nominal ratio: K   VS

GATE ACADEMY®

49

Instrument Transformer

3.1 Ratio Error K R Ratio Error  100 % R I n  S [ RP cos   X P sin ]  I  rP  I  X P n R VS

where,

RP  n 2 rS  rP X P  n 2 X S  xP ,   tan 1

xl rl

3.2 Phase error : IS [ X P cos   RP sin ]  I  xP  I  rP n  nVS Objective & Numerical Ans Type Questions :

Q.1

A 50 Hz bar primary CT has a secondary with 500 turns. The secondary supplies 5 A current in to a purely resistive burden of 1

Q.5

The magnetizing ampere turns is 200. The phase angle between the primary and secondary current is [GATE-2004, IIT-Delhi]

Q.2

Q.3

Q.4

(A) 4.60

(B) 85.40

(C) 94.60

(D) 175.40

(B) 45.0 Wb

(C) 22.5mWb

(D) 100.0mWb

The primary of a 200/1 A, 5 VA, 0.8 pf current transformer (CT) carries 100 A. The secondary current is 0.495 A. the ratio error of the CT is [GATE-2003, IIT-Madras] (A) – 1.0% (B) – 0.5% (C) +0.5% (D) +1.0% A 500A/5A, 50 Hz current transformer has a bar primary. The secondary burden is a pure resistance of 1 and it draws a current of 5 A. If the magnetic core requires 250 AT for magnetization, the percentage ratio error is [GATE-2003, IIT-Madras]

(B) – 10.56

(C) 11.80

(D) – 11.80

A 200/1 Current transformer (CT) is wound with 200 turns on the secondary on a toroidal core. When it carries a current of 160 A on the primary, the ration and phase errors of the CT are found to be – 0.5% and 30 minutes respectively. If the number of secondary turns is reduced by 1the new ratio error (%) and phase error (min) will be respectively [GATE-2006, IIT-Kharagpur]

The core flux in the CT of above question under the given operating conditions. [GATE-2004, IIT-Delhi] (A) 0

(A) 10.56

Q.6

(A) 0.0, 30

(B) – 0.5, 35

(C) – 1.0, 30

(D) – 1.0, 25

The total impedance of the secondary winding, leads and burden of a 5 A CT is 0.01 . If the fault current is 20 times the rated primary current of the CT, the VA output of the CT is _______. [GATE-2019, IIT-Madras]

Practice (objective & Num Ans) Questions :

Q.1

A current transformer has a phase error of

 30 . The phase angle between the primary and secondary currents is (A) 30

(B) 1770

(C) 1800

(D) 1830

Electrical & Electronic Measurements [Workbook]

In using instrument transformers, care should be taken not to open circuit the (A) primary of a voltage transformer when the secondary is connected to the rated load (B) secondary of a voltage transformer when the primary is energized with the rated voltage (C) primary of a current transformer when the secondary is connected to the rated load (D) secondary of a current transformer when the primary is carrying the rated current In potential transformers, the secondary turns are increased slightly and the primary and secondary windings are wound as closely as possible to compensate for (A) Phase angle and ratio error, respectively (B) Ratio and phase angle error, respectively (C) Any eddy current loss and hysteresis loss, respectively (D) The hysteresis loss and eddy current loss, respectively

Q.2

Q.3

GATE ACADEMY®

50

(C) Voltage, current and power factor of secondary winding circuit (D) None of the above Statement for Linked Questions 2 and 3

Q.2

1000 A, 50 Hz current transformer has a 5 purely resistive secondary burden of 1.6  . The primary winding has a single turn. The iron loss in the core is 1.5 W at full load. The leakage reactance is to be neglected. The core flux in the CT at full load is _____

Q.3

μWb Current ratio error on full load is _____ %

A

Q.4

Q.5

Assignment (objective & Num Ans) Questions :

The burden of current transformers is expressed in terms of (A) Secondary winding current (B) VA rating of transformer

Q.1

1000 A is 5 operating at full primary current and with a secondary burden of non-inductive resistance of 1  . The exciting current is 1 A at a power factor of 0.4, _____degree is the phase angle error? A 50 Hz, bar primary CT has a secondary with 300 turns. The secondary supplies 5 A current into a burden which consists of a resistance and reactance of 1.5  and 1.0  respectively. The magnetizing mmf is 100 A and the iron loss is 1.2 W. The phase angle between the primary and secondary is _____degree.

A ring core transformer with ratio

Answer Keys

Objective & Numerical Answer Type Questions 1.

D

6.

100

2.

B

3.

A

4.

B

5.

A

5.

177.66

Practice (Objective & Numerical Answer) Questions 1.

B

2.

D

3.

B

Assignment (Objective & Numerical Answer) Questions 1.

B

2.

180

3.

-3.75

4.

0.0525



8

Error Analysis

Formulas & Logics 1. Classification of error 1.1 Absolute error/static error : Deviation between measured value and true value of quantity under measurement is called absolute error it is also known as limiting or guarantee error,

  Am  AT where  A  absolute error, Am  measured value, AT  True value. 1.2 Relative error :

% r 

Am  AT 100% AT

%r in measured scale 

Full scale value  %Full scale error Measured scale

1.3 Sum of quantities :

Let,

X 1  a  r1 X 2  b   r2 X 3  c   r3

For summation or difference  X1  X 2  X 3 b c  a   r1   r2   r3  % r    abc abc  a b  c 1.4 Multiplication of quantities :

X 1  a   r1 , X 2  b   r2 , X 3   r3

Let,

X  X1  X 2  X 3 % r  ( r1   r2   r3 )%

1.5 Division of quantities :

X 1  a   r1 , X 2  b   r2 , X 3  c   r3

Electrical & Electronic Measurements [Workbook]

X

GATE ACADEMY®

52

X1 X 2 X3

% r  ( r1   r2   r3 )% 1.6 Error due to composite factor :

Let,

X 1m X 3p X 1m X 2n X or X 3p X 2n % r  (m r1  n r2  p r3 )%

2. Statistical analysis of errors

Consider a set of readings (i.e. X1, X 2 , X 3...... X m ) of an instrument. The various terms used in statistical analysis are as follows : 2.1 Mean value of readings : X  X 2  X 3  ....... X n X  1 n 2.2 Deviation : d1  X 1  X , d 2  X 2  X , d n  X n  X 2.3 Mean deviation : d

d1  d 2  d 3  ..... d n n

2.4 Range of error : X  X 2  X 3  ..... X n X avg  1 n

Range of errors   where,

[ X d max  X d min ] 2

X d max  X max  X avg X d min  X avg  X min

2.5 Average range of error : X avg 

X d max  X d min

2 2.6 Standard deviation : n

S.D.   

 di i 1

n

S.D. 

 di

n

2

for n  20

2

i 1

n 1

2.7 Variance (V) 2 2 V  (S.D.)  

for n  20

GATE ACADEMY®

53 n

V

 di

for n  20

n n

V

2

i 1

 di

Error Analysis

2

i 1

for n  20

n 1

2.8 Probable error (r) :

Probable error is a measure of precision of instrument it is directly proportional to the standard deviation and it is given by, r  r  0.6745

2.9 Standard deviation of combination of quantities : 2

2

2

 X   X   X  2 2 2 X    ( X 3 )  .....  ( X1 )    ( X 2 )    X 1   X 2   X 3 

2.10 Un-certainty due to combination of quantities : 2

2

2

 X  2  X  2  X  2 Wx    Wx 3  ........  Wx1    Wx 2    X 1   X 2   X 3  Objective & Numerical Ans Type Questions :

Q.1

A current of [2  2 sin(314t  300 )  2 2 cos(952t  450 )]

Q.4

Q.2

(B) (2  3 2) A  1%

(C) 3A  1.67%

(D) 2A  0.5%

Q.3

[GATE-2002, IISc-Bangalore]

(A)  3.75%

(B)  1.25%

(C)  12.5%

(D)  0/125%

The current ‘I’ through a resistance R is measured with the following uncertainties I  4A  0.5% , R  100   0.2% . If power is computed from these two measured quantities, the uncertainty in the power computed will be

(C) 0.7%

(D) 1.2%

A large number of 230 resistors are standard deviation of

4

and 110 

resistor with a standard deviation of 3  . The standard deviation of the

230

resistors thus formed will be [GATE-2003, IISc-Bangalore]

The radius of a sphere is given as (40.0  0.5) mm. The estimated error in its mass is :

(B) 0.29%

obtained by combining 120  resistor with a

Amp is measured with a thermocouple type, 5A full scale, class 1 meter. The meter reading would lie in the range, [GATE-1999, IIT-Bombay] (A) 5A  1%

(A) 0.01%

Q.5

(A) 3.5

(B) 5.0

(C) 7.0

(D) 12.0

Suppose that resistors R1 and R2 are connected in parallel to give equivalent resistor R. If resistor R1 and R2 have tolerance of 1% each, the equivalent resistor R for resistors R1  300  and R2  200  will have tolernate of [GATE-2014, IIT-Kharagpur] (A) 0.5% (B) 1% (C) 1.2% (D) 2%

Electrical & Electronic Measurements [Workbook]

Q.6

Consider the ammeter-voltmeter method of determining the value of the resistance R using the circuit shown in the figure. The maximum possible errors of the volt meter and ammeters are known to be 1% and 2% of their readings, respectively. Neglecting the effects of meter resistances, the maximum possible percentages error in the value of R determined from the measurements, is_________%. [GATE-2015, IIT-Kanpur]

Source Vi

Q.7

Q.8

+ Voltmeter V -

R

+ A Ammeter -

A temperature in the range of 400 C to 550 C is to be measured with a resolution of

0.10 C . The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is [GATE-2016, IISc-Bangalore] (A) 8 (B) 10 (C) 12 (D) 14 A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 V respectively. A second voltage V2 , which is independent of V1 , is measured 200 times and its average and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3  V1  V2 . Then the standard deviation of V3 in volt is ________.

Q.9

[GATE-2016, IISc-Bangalore] The following measurements are obtained on a single phase load : V  220V  1%,

I  5.0A  1% and W  555W  2% . If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ________. (Give answer up to once decimal place.) [GATE-2017, IIT-Roorkee] Q.10 The resistance of a resistor is measured using a voltmeter and an ammeter. The

GATE ACADEMY®

54

voltage measurements have a mean value of 1 V and standard deviation of 0.12 V while current measurements have a mean value of 1 mA with standard deviation of 0.05 mA. Assuming that the errors in voltage and current measurements are independent, the standard deviation of the calculated resistance value is ________  . [GATE-2019, IIT-Madras] Q.11 A (0–25) A ammeter has a guaranteed accuracy of 1 percent of full scale reading. The current measured by this ammeter is 10A. The limiting error in percentage for this instrument is (A) 2.5% (B) 0.5% (C) 80% (D) 0.025% Practice (objective & Num Ans) Questions :

Four ammeters M1, M2, M3 and M4 with the following specification are available. Full scale Accuracy Instrument Type value % of FS (A) 0.10 20 M1 1 3 digit 2 dual slope 0.20 M2 PMMC 10 0.50 M3 Electro5 dynamic 1.00 M4 Moving1 iron A current of 1A is to be measured. To obtain minimum error in the reading. One should select meter (A) M1 (B) M2 (C) M3 (D) M4 Q.2 Resistance R1 and R2 have respectively Q.1

nominal values of 10  and 5  and tolerance of 5% and 10% . The range of values for the parallel combination of R1 and

R2 (A) 3.077  to 3.636  (B) 2.805  to 3.371 

GATE ACADEMY®

Q.3

55

(C) 3.237  to 3.678 

(A) [123.50, 136.50] (B) [125.89, 134.12]

(D) 3.192  to 3.43 

(C) [117.00, 143.00] (D) [120.25, 139.75]

A variable  is related to three other xy . The variables are variables x, y, z as   z measured with meters of accuracy 0.5% reading, 1% of full scale and 1.5% reading. The actual readings of three meters are 80, 20 and 50 with 100 being the full scale valve for all three. The maximum limiting error in the measurement of  will be. (A)  0.5% rdg (B)  5.2% rdg (C)  6.7% rdg

Q.4

Q.6

Vs

Rm

Ideal Voltmeter

measured voltage

(B) Rs only

Rs Rm

(D) Rm  Rs

(C)

When the Wheatstone bridge shown in the figure is used to find the value of resistor RX , the galvanometer G indicates zero current when R1  50 ,

R2  65  and

-

2

2

2

2

Two

resistance

of

100   1%

and

200   3% are connected in series. Find the % error and range of equivalent resistance of combination? Assignment (objective & Num Ans) Questions :

Q.1

The resistance of a circuit is found by measuring current flowing and the power fed into the circuit. If the limiting errors in the measurement of power and current are 1.5% and 1.0% respectively, the limiting error in the measurement of resistance will be

G

V

2

Q.8

R2

+

2

An ammeter has a full scale value of 100 A has full scale error of 2%. Find the % of error. If it is measuring 50 A

range of RX in ohms will be

Rx

2

Q.7

tolerance on its nominal value of 100  , the

R3

2

 R   R  (D)    R1    R2  R1   R2 

R3  100 . If R3 is known with ± 5%

R1

these

 R   R  (C)    R2    R1  R1   R2 

Ve is a function of, Vs

(A) Rm only

When

 R   R  (B)   R1    R2   R2   R1 

V

Let Ve be the difference between Vs and the

respectively.

 R   R  (A)   R1    R2   R1   R2 

Non-ideal Voltmeter

Ideal Voltage source

R2 .

resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

(D)  7.0% rdg

Rs

Two resistors with nominal resistance values R1 and R2 have additive uncertainties R1 and

Consider a non-ideal voltage source whose output voltage is measured by a non-ideal voltmeter as shown below

Non-ideal Voltage Source

Q.5

Error Analysis

Q.2

(A) 1%

(B) 1.5%

(C) 2.5%

(D) 3.5%

The percentage limiting error, in the case of an instrument reading of 8.3 V with a 0 to 150 voltmeter having a guaranteed accuracy of 1% full-scale reading is

Electrical & Electronic Measurements [Workbook]

Q.3

Q.4

(A) 1.810% (B) 0.181% (C) 18.10% (D) 0.0018% A 150V moving iron voltmeter of accuracy class 1–0 reads 75V when used in a circuit under standard condition. The maximum possible percentage error in the reading is (A) 0.5 (B) 1.0 (C) 2.0 (D) 4.0 The current flowing through the resister R is as indicated in the given figure. The computed value of power is

GATE ACADEMY®

56

Q.8

(A) 50  2%

(B) 50  3%

(C) 50  5%

(D) 50  10%

A voltage waveform shown in the given figure is applied to an ideal full-wave rectifier voltmeter. The voltmeter is calibrated to read the RMS values of sinewaves. The voltmeter will read 100 V 50 V

t - 50 V

I = 2 ± 0.2 A

-100 V R = 100 ± 0.2 W

Q.5

Q.6

Q.7

(A) 400 ± 0.42 W (B) 400 +4.60 W (C) 400 ± 8.8 W (D) 400 ± 1065 W The most serious source of error in ac bridge measurement is (A) eddy currents (B) leakage currents (C) residual imperfectness (D) stray fields A peak-responding ac voltmeter employing a half-wave precision rectifier has been calibrated to give a reading of 1 V for 1 V rms sinusoidal input. For IV dc input, the meter reading will be (A) 0.707 V (B) 0.707 V or 0 V (C) 1.414 V (D) 1.414 V or 0 V The arms of a Wheatstone bridge are shown in the given figure. For the balanced condition, the least tolerance value of R4 will be R1 = 10 ± 2 % W

R3 = 100 ± 3% W

R2 = 5 ± 5% W

R4 W

(A)

50 V 2

(C) 100 V Q.9

(B)

100 V 2

(D) 111 V

The circuit given in the figure, the limiting error in the power dissipation ‘ I 2 R ’ in the resistor R is +

-

R = 100 ± 0.2% W

I = 2 ± 5% A

(A) 1.2 %

(B) 5.2 %

(C) 10.2 %

(D) 25.2 %

Q.10 A current of 10A  2% is passed through a

resistance of 100   1 . Then find the error in the voltage measured across the resistor? Q.11 A current of 5A  0.2A is passed through

resistance of value 20   1 . Find the power consumed by the resistance and the error in the power consumed.

GATE ACADEMY®

57

Error Analysis

Answer Keys

Objective & Numerical Answer Type Questions 1.

C

2.

A

3.

D

4.

B

5.

B

6.

3

7.

B

8.

2.5

9.

4

10.

130

11.

A

5.

A

Practice (Objective & Numerical Answer) Questions 1.

D

2.

A

3.

6.

A

7.

4%

8.

D

4.

C

7 % , 300  7  3

Assignment (Objective & Numerical Answer) Questions 1.

D

2.

C

3.

C

4.

C

5.

B

6.

A

7.

D

8.

D

9.

C

10.

 3%

11.

500 W, 13 % 

9

Q ‐ Meter

Formulas & Logics 1. Q Meter I R Coil L

V

C

Vc Voltmeter

Fig. Circuit diagram  Q-meter works on the principle of series resonance. where L  Inductance of coil, R  Resistance of coil C  Distributed capacitance of coil

At series resonance,

X L  XC Voltage across capacitor : VC  IX C 

VC  QV So,

X X V XC  V C  V L R R R

XC X L    Q   R R  

VC  Q

Capacitor voltage is directly proportional to Q factor.

GATE ACADEMY®

59

Q ‐ Meter

2. Application of Q-Meter 2.1 Measurement of Q-factor of Test Coil : Test coil

T1

VS

Rh

L

T2

R

T3 Rsh

V

VC

C

T4

Fig. Circuit diagram

True Quality factor :

Qtrue 

QL R

Measured Quality Factor : Qmeasured  Qmeasured 

XL R  Rs h

Q XL  true R  R  R 1  sh  1  sh R R  

 R  Qtrue  Qmeasured 1  sh  R  

To obtain Qtrue  Qmeasured , Rsh should be low i.e. in m range. 2.2 Measurement of Unknown Capacitance : Test coil

T1 Rh

VS

L

R

T2

T3 Rsh

V

CT

C

VC

T4 Fig. Circuit diagram  A test capacitor is connected between T3 and T4 and by varying the capacitor C  C1 we obtain resonant frequency. f1 

1 2 L(C1  CT )

…(i)

 By removing CT and varying the capacitor C  C2 circuit is resonated at same frequency f2 

1 2 LC2

…(ii)

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

60

Equation (i) and (ii) are same

1 1  2 L(C1  CT ) 2 LC2

[ f1  f 2 ]

C1  CT  C2 CT  C2  C1 2.3 Measurement of distributed capacitance of the coil :

Test coil R

Rh

VS

T1

L

Cd

Rsh V

T2 T3 T4

C

VC

Fig. Circuit diagram Assume Rsh is less, When C is adjusted to C1 and resonance occurs at f1 ,

f1 

1 2 (C1  Cd ) L

…(i)

Again C is adjusted to C2 and resonance occurs at n f1 ,



n f1 

1 2 (C2  Cd ) L

From equation (i) and (ii) n 2 f12  



n2 1  2 2 4 (C1  Cd ) L 4 (C2  Cd ) L

n2 1  C1  Cd C2  Cd Cd 

C1  n 2C2 n2  1

…(ii)

GATE ACADEMY®

61

Q ‐ Meter

a capacitance of 990 pF. The second resonance at 2  2  106 rad/s is obtained

Objective & Numerical Ans Type Questions :

Q.1

A Q-meter having an insertion resistance of 0.01  is used to measure the inductance of

with a 240 pF capacitance. The value of the inductance (in mH) of the coil is (up to one decimal place) ________. [GATE-2018, IIT-Guwahati]

a coil. Resonance occurs at an angular frequency of 106 rad/s with a capacitance of 40 pF. The inductance of the coil is [GATE-2004, IIT-Delhi] (A) 250 mH (B) 2.5 mH (C) 25 mH Q.2

Practice (objective & Num Ans) Questions :

Q.1

A very low-loss coil is tested with Q-meter and the distributed (self) capacitance of the coil is found to be 820 pF. Resonance

(D) 0.25 mH

Figure shows a circuit which has a coil of resistance R and inductance L. At resonance, the Q-factor of the coil is given by [GATE-2005, IIT-Bombay]

occurred at an angular frequency  of 106 rad./s with a capacitance of 9.18 nF. The inductance of the coil is

Q.2

 V  V0  (A)    V 

Q.3

Q.4

Q.5

(B) 100 H

(C) 100 nH

(D) 100 mH

A reading of 120 is obtained when a standard inductor was connected in the circuit of a Q–meter and the variable capacitor is adjusted to a value of 300 pF. A 0.02 , 250 H lossless capacitor of

V  (B)  0  V 

 V  V0  V  (C)  (D)     V0   V0  The Q-meter works on the principle of [GATE-2005, IIT-Bombay] (A) Mutual inductance (B) Self inductance (C) Series resonance (D) Parallel resonance A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with a capacitance of 110 PF. When the frequency is doubled, the capacitance required for resonance is 20 Pf. The distributed capacitance of the coil in Pico farad is _______. [GATE-2016, IISc-Bangalore] A high Q coil having distributed (self) capacitance is tested with a Q-meter. First resonance at 1  106 rad/s is obtained with

(A) 100 pH

unknown value Cx

is then connected in

parallel with the variable capacitor and the same reading was obtained when the variable capacitor is readjusted to a value of 200 pF. The value of Cx in pF is

Q.3

(A) 100

(B) 200

(C) 300

(D) 500

In the given circuit, C0

is the distributed

capacitance of the coil and C is the tuning capacitor. If C  C1 for the fundamental frequency and C  C2

for the second

harmonic, then the value of C0 can be expressed as a L

C0 R

C(Tuning capacitor) b

Electrical & Electronic Measurements [Workbook]

C1  2C2 C  4C2 (B) C0  1 3 3 C1  C2 (C) C0  (D) C0  C1  2C2 3 A coil is tuned to resonance at 1 MHz with a resonating capacitance of 72 pF. At 500 kHz the resonance, is obtained with a resonating capacitance value of 360 pF. The selfcapacitance of the coil is

(A) C0 

Q.4

(A) 12 pF

(B) 24 pF

(C) 36 pF

(D) 72 pF

GATE ACADEMY®

62 Q.3

Q.4

A Q-meter is supplied with an oscillator having a 500 mV output voltage. While testing an unknown inductor, the voltage across the variable capacitor of the Q-meter, measured by a digital voltmeter, is obtained as 10 V. The Q-factor of the inductor is (A) 5

(B) 10

(C) 20

(D) 0.05

Consider the following statements : If a high Q parallel resonant circuit is loaded with a resistance

Assignment (objective & Num Ans) Questions :

1. The circuit impedance reduces

Q.1

2. The resonant frequency remains the same

An inductor tunes at 200 kHz with 624 pF capacitor and at 600 kHz with 60.4 pF capacitor. The self-capacitance of the inductor would be

Q.2

3. The bandwidth reduces

(A) 8.05 pF

(B) 10.05 p

Which of the above statements is/are correct?

(C) 16.10 pF

(D) 20.10 pF

(A) 3 only

(B) 2 only

(C) 1 only

(D) 1, 2 and 3

A coil is tuned to resonance at 500 kHz with a resonating capacitor of 36 pF. At 250 kHz, the resonance is obtained with resonating capacitor of 160 pF. What is the selfcapacitance of the coil? (A) 2.66 pF

(B) 5.33 pF

(C) 8 pF

(D) 10.66 pF

Answer Keys

Objective & Numerical Answer Type Questions 1.

C

2.

D

3.

C

4.

10

5.

1

Practice (Objective & Numerical Answer) Questions 1.

B

2.

A

3.

B

4.

B

Assignment (Objective & Numerical Answer) Questions 1.

B

2.

B

3.

C

4.

D 

10

Cathode‐Ray Oscilloscope (CRO)

Formulas & Logics

Vs

e Vr

Fig. Circuit diagram of CRO

Fig. Sweep Generator is connected to Horizontal plates  CRT works on the principle of thermionic emission i.e. emission of electrons from a heated surface called electron gun made of tungsten.  Cathode is cylindrical in shape at the end of which a layer of Barium (Ba) and strontium (Sa) oxide is deposited in order to have high emission of electrons at moderate temperature.  The electrons emitted from cathode passes through a cylindrical shaped control grid of Nickel. The control grid is given by a negative potential in order to control the number of electrons emitted from cathode.

GATE ACADEMY®

64

Electrical & Electronic Measurements [Workbook]

 Velocity or acceleration of emitted electron are controlled by changing the anode potential of pre and post accelerating anode.  Focusing anode uses Electrostatic focusing for the focus control of electron beam. It works on the principle of Double concave electron lens.  In normal Horizontal deflecting mode are supplied with output of a sweep generator.

 Vertical deflecting plates are applied with external test signal (output of function generator).  Astigmatism is used for fine focus control of the electron beam on the screen by applying small DC potential to the horizontal and vertical deflecting plate.  Screen is coated with phosphorous which converts heat energy into light energy. Some elements called activators are added to the coating of phosphor in order to increase luminous efficiency, spectral emission. Ex : Silver, Manganese, Copper and Chromium.  Aquadag coating is used to collect the secondary emitted electrons and to maintain neutral condition in the CRT. 1. Electrostatic Deflection Vertical deflection plate V

Parabolic path d

D d ld L

Screen

Deflection on screen : L  ld Vd D 2d Va Where,

D  Deflection height on screen, L  Distance between center of deflecting plate to screen

Vd  Deflecting plate voltage, Va  Anode voltage d  Distance between plates S  Deflection sensitivity

S

D L  ld  Vd 2d Va

Deflection factor : G 

1 2 d Ea  S L  ld

2. Oscilloscope Amplifier 2.1 Vertical Amplifier : 0.35 BW  tr where,

BW = Bandwidth and tr = Rise time for amplifier.

GATE ACADEMY®

65

Cathode‐Ray Oscilloscope (CRO)

2.2 Horizontal Amplifier :  Horizontal Amplifier serves to the two proposes,  In normal mode it amplifies the output of sweep generator.  In dual mode it amplifies the signal connected at x-input channel. 3. Lissajous Pattern 3.1 Finding



If Lissajous pattern is given :

(i) If Lissajous pattern is in 1st and 3rd quadrant y2

Vy

y1 x1

x2

Vx

x  y  0    sin 1  1  or sin 1  1  or 360    x2   y2 

(ii) If Lissajous pattern is in the 2nd and 4th quadrant Vy

y2 y1

x1

x     1800  sin   1   x2 

x2

Vx

y  0 1800  sin   1  or 360   y  2 180  



180  



Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

66

Objective & Numerical Ans Type Questions :

The phase angle between the signals, is

Q.1

(A) cos1 ( A/B)

(B) tan 1 ( A/B)

(C) sin 1 ( A/B)

(D) ( A/B)

A lissajous pattern, as shown in figure below, is observed on the screen of a CRO when voltages of frequencies fx and f y are

Q.5

applied to be X and Y plates respectively. f x : f y is then equal to

A double beam CRO has a band-width of 10 MHz. two signals, 3 and v1 (t )  10sin (2 20 10 t )

v2 (t )  10sin (2 20 106 t ) are applied to

[GATE-1994, IIT-Kharagpur]

the two channels. If P1 and P2 are the peak-

Q.2

Q.3

(A) 3:2 (B) 1:2 (C) 2:3 (D) 2:1 A certain oscilloscope with 4 cm screen has its own sweep output fed to its input. If the X and Y sensitivity are, then oscilloscope will display a [GATE-1995, IIT-Kanpur] (A) Triangular wave (B) Diagonal line (C) Sine wave (D) Circle An oscilloscope input impedance consist of 1M resistance connected in parallel with

100 pF capacitor. A compensated 20:1 attenuator is obtained by connecting a parallel combination of [GATE-1999, IIT-Bombay] 100 (A) 19 M and pF 19 100 (B) 20 M and pF 20 (C) 19 M and 1900 pF

(C) P1  20, P2  20 Q.6

(D) P1  20, P2  20

A symmetrical square wave of frequency 25 kHz and a peak-to-peak amplitude of 10 V is fed to Y -input of a signal channel oscilloscope. The screen appears as shown in figure. The X and Y sensitivity and the trigger settings respectively are [GATE-2004, IIT-Delhi]

(A) 5 s/cm, 2 V/cm and  ve slope (B) 5 s/cm, 2 V/cm and  ve slope (C) 10 s/cm, 1 V/cm and  ve slope (D) 20 s/cm, 2 V/cm and  ve slope Q.7

The simultaneous application of signal x(t ) and y (t ) to the horizontal and vertical

(D) 20 M and 2000 pF Q.4

to-peak values of the signals displayed, then [GATE-2001, IIT-Kanpur] (A) P1  20, P2  20 (B) P1  20, P2  20

The elliptical Lissajous pattern shown in figure was observed from two sinusoidal sign al sources of same frequency on a CRO [GATE-2000, IIT-Kharagpur]

plates, respectively of an oscilloscope, produces a vertical figure of 8-display. If P and Q are constant and x(t )  P sin(4t  300 ) these y (t ) is equal to [GATE-2005, IIT-Bombay] (A) Q sin(4t  300 )

2A 2B

(B) Q sin(2t  150 ) (C) Q sin(8t  600 ) (D) Q sin(4t  300 )

GATE ACADEMY®

Q.8

67

Cathode‐Ray Oscilloscope (CRO)

The input impedance of a CRO is equivalent to a 1M resistance in parallel with a 45pF capacitance. It is used with a compensated 10 to 1 attention probe. The effective input capacitance at the probe [GATE-2009, IIT-Roorkee]

Q.9

(A) 4.5 pF

(B) 5 pF

(C) 45 pF

(D) 450 pF

A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHz. The frequency of the vertical input is [GATE-2017, IIT-Roorkee]

(A) 1.5 kHz

(B) 2 kHz

(C) 3 kHz

(D) 4.5 kHz

Q.10 In an oscilloscope screen, linear sweep is applied at the [GATE-2014, IIT-Kharagpur]

(A) Vertical axis

(A) 5 V, 1 ms (B) 5 V, 2 ms (C) 7.5 V, 2 ms (D) 10 V, 1 ms Q.12 The x and y sensitivity of an analog oscilloscope are set as 2 ms/cm and 1 V/cm respectively. The trigger is set at 0 V with negative slope. An input of 0 2 cos (100t  30 ) V is fed to the y input of the oscilloscope. The wave from seen on the oscilloscope will be [GATE-2006, IISc-Bangalore] (A)

(B) Horizontal axis (C) Origin (D) Both horizontal and vertical axis Q.11 The time/div and voltage/div axes of an oscilloscope have been erased. A student connects a 1 KHz, 5 V p - p square wave

calibration pulse to channel 1 of the scope and observes the screen to be as shown in the upper trace of the figure. An unknown signal is connected to channel 2 (lower trace) of the scope. If the time/div and V/div on both channels are the same, the amplitude ( P  P ) and period of the unknown signal

(B)

(C)

are respectively. [GATE-2006, IIT- Kharagpur]

(D)

Electrical & Electronic Measurements [Workbook]

Q.13 In an analog signal channel cathode ray oscilloscope (CRO), the x and y sensitivity

are set as 1 ms/div, and 1 V/div, respectively. The y -input is connected to a voltage signal 4 cos(200t  45 ) V. The 0

GATE ACADEMY®

68

Q.14 The two signals S1 and S2, shown in figure, are applied to Y and X deflection plates of an oscilloscope. V

S1

1

trigger source is internal, level chosen is zero and the slope is positive. The display seen on the CRO screen is [GATE-2010, IIT- Guwahati]

V 1

T

2T

T

2T

t

S2

(A) t

The waveform displayed on the screen is [GATE-2014, IIT-Kharagpur]

(A)

(B)

Y

1

1

(B)

Y

X

X

–1

(C)

–1

(D)

Y

Y

1

(C)

–1

1 X

X –1

Q.15 The slope and level detector circuit in a CRO has a delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line [GATE-2017, IIT- Roorkee] of

(D)

(A) 150 ns has to be inserted into the ychannel (B) 150 ns has to be inserted into the xchannel (C) 150 ns has to be inserted into both x and y channel (D) 100 ns has to be inserted into both x and y channel

GATE ACADEMY®

69

Q.16 A voltage of 6 cos(100t ) V is fed as y-

input to a CRO. The waveform seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are respectively [GATE-2018, IIT- Guwahati]

Cathode‐Ray Oscilloscope (CRO) Practice (objective & Num Ans) Questions :

Q.1

The relationship between Ts  rise time of the signal, T0 = rise time of the oscilloscope, is TD (rise time of the signal observed on the oscilloscope) equal to

(A) 1 V/div and 1 ms/div (B) 1 V/div and 2 ms/div (C) 2 V/div and 1 ms/div (D) 2 V/div and 2 ms/div Q.17 A CRO screen has ten division on the horizontal scale. If a voltage signal 5sin(314t  450 ) is examined with a time base setting of 5 m sec/div, the number cycle of signal displayed on the screen will be [GATE-1993, IIT- Bombay] (A) 0.5 cycles (B) 2.5 cycles (C) 5 cycles (D) 10cyles Q.18 The probes of a non-isolated two channel oscilloscope are clipped to points A, B and C in the circuit of the adjacent figure. Vin is

Q.2

Q.3

Vin

C

Ch2

Two in phase 50 KHz sinusoidal wave forms of unit amplifier are fed amplitude are fed into channel – 1 and channel – 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other setting are exactly the same for both the channels. What would be observed if the oscilloscope is operated in X  Y mode?

A reading of 120 is obtained when standard inductor was connected. The circuit of a Q meter and the variable capacitor is adjusted to a value of 300 pF . A lossless capacitor of unknown value Cx is then connected in parallel with the variable capacitor when the variable capacitor is readjusted to a value of

200 pF . The value of Cx in pF is

B

L

1

(D) A straight line inclined at 450 with respect

[GATE-2007, IIT- Kanpur] Ch1

(D) [Ts2  T02 ] 2

(C) A parabola

and Ch2 respectively are connected to the

R

(C) Ts  T0

(B) An ellipse

on the right. Then the “signal” and “Ground” probes S1 , G1 and S 2G2 of Ch1

A

(B) [Ts3  T02 ] 2

(A) A circle of unit radius

a square wave of a suitable low frequency. The display on Ch1 and Ch2 are as shown

points :

1

(A) Ts  T0

Q.4

(A) 100

(B) 200

(C) 300

(D) 500

An oscilloscope screen displayed an line inclined 450 . Its Y input is a sine wave of frequency f then Y input should be (A) Sine wave of frequency f and 00 phase shift with Y input.

(A) A, B, C , A

(B) A, B, C , B

(C) C , B, A, B

(D) B, A, B, C

(B) Sine wave of frequency f and 450 phase shift with Y input.

GATE ACADEMY®

70

deflecting plates 1 cm long and 0.5 cm apart, when screen is 30 cm from the center of the plates is (A) 300 V (B) 200 V (C) 100 V (D) 75 V

(C) Sine wave of frequency f and 900 phase shift with the Y input. (D) Saw tooth wave of frequency f . A CRO probe has an impedance of 500k

Assignment (objective & Num Ans) Questions :

Q.1

measured voltage will be P 100 K 10 V rms 100 KHz

Q.6

500 kΩ

To CRO through probe

(A) 3.53 V

(B) 4.37 V

(C) 4.54 V

(D) 5.00 V

In a single beam signal trace analog oscilloscope a delay line is inserted between (A) X input and X plate

Q.2

(B) Y input and Y plate (C) X input and trigger circuit (D) Y input and the trigger circuit Q.7

Q.8

Two sinusoidal signals having the same amplitude and frequency are applied to tile X and Y inputs of a CRO. The observed Lissajous figure is a straight line. The phase shift between the two signals would be (A) Zero (B) 90 degrees (C) Either zero or 180 degrees (D) Either 90 degrees or 270 degrees Voltages Vy  100sin1000t and Vx  50 sin1000t are connected to Y and X

terminals of a CRO, respectively. What is the shape of the figure seen on the CRO?

Q.9

(A) A circle

(B) A straight line

(C) An ellipse

(D) A parabola

An input voltage required to deflect a beam through 3 cm in a Cathode Ray Tube having an anode voltage of 1000V and parallel

Q.3

A dual trace oscilloscope is set to operate in the alternate mode. The control input of the multiplexer use in the Y- circuit is fed with a signal having a frequency equal to (A) The highest frequency that the multiplexer can operate properly. (B) Twice the frequency of the time base (sweep) oscillator. (C) The frequency of the time base (sweep) oscillator. (D) Half the frequency of the time base (sweep) oscillator. In an oscilloscope screen, linear sweep is applied at the (A) Vertical axis (B) Horizontal axis (C) Origin (D) Both horizontal and vertical axis The linear sweep for the time base in an oscilloscope has deviation from its nominal waveform. The nominal (dashed line) and actual (solid line) sweep waveform are shown in the following figure. Retrace Nominal

Sweep start time

Actual time

1.3T

probe is used to measure the voltage between P and Q as shown in figure. The

1.15T

in parallel with a capacitance of 10PF . The

1.1T

Q.5

T

Electrical & Electronic Measurements [Workbook]

A 5 V p  p sine wave with a frequency of 1 kHz will be measured on the oscilloscope as a sine wave with (A) 4.45 V p  p and 1 kHz frequency (B) 5 V p  p and 1 kHz frequency (C) 5 V p  p and 1.1 kHz frequency (D) 5 V p  p and 1.15 kHz frequency

GATE ACADEMY®

Q.4

Two signals of peak-to-peak voltages 5 V and 2 V are being fed to channel 1 and channel 2, respectively of an oscilloscope with a single time base. The vertical sensitivity of both channels is 1 V/division. The two sine waves have identical frequency and phase. The trigger is on manual mode and triggers at a level of +1.25 V on channel 1, as shown in the figure below :

Which of the following figures correctly depicts the trace seen in channel 2?

Q.5

Q.6

(A) P (B) Q (C) R (D) S A Lissajou’s pattern observed on an oscilloscope is stationary and has 5 horizontal tangencies and 2 vertical tangencies. If the frequency of horizontal input is 1,000 Hz, then frequency of vertical input is (A) 2500 Hz (B) 500 Hz (C) 400 Hz (D) 2000 Hz An unknown voltage is applied to the horizontal deflection plate of a CRO, which shifts the spot by 5 mm towards the right. If the deflection sensitivity is 0.05 mm/V, then the applied unknown voltage is ________ V.

71

Cathode‐Ray Oscilloscope (CRO)

Trigger pulses in the CRO are used (A) To generate high voltage required for the CRT (B) To synchronize the input with the time base generator (C) To synchronize the input and the vertical amplifier (D) To generate low voltages required for the CRT Q.8 Which of the following measurements can be made using Lissajou’s figures ? 1. Frequency 2. Phase difference 3. Time interval between pulses 4. Pulse width 5. Fundamental and higher harmonic components Select the correct answer using the code given below : (A) 1 and 2 (B) 2 and 3 (C) 3 and 4 (D) 4 and 5 Q.9 In a CRO astigmatism is (A) A source of generating fast electrons (B) A medium for absorbing secondary emission electrons (C) An additional focus control (D) A time-delay control in the vertical deflection system Q.10 A screen pattern oscillogram, shown in the figure below is obtained when a sine-wave signal of unknown frequency is connected to the vertical input terminals, and at the same time, a 600 Hz sine-wave voltage is connected to the horizontal input horizontal of an Q.7

Vertical axis

Horizontal axis

What is the value of unknown frequency? (A) 300 Hz (B) 400 Hz (C) 600 Hz (D) 900 Hz

Electrical & Electronic Measurements [Workbook]

Q.11 In an oscilloscope, two Lissajous figure ( X ) and (Y ) are observed. This indicates that ratio of vertical input signal frequency to that of horizontal input frequency are

(X)

(Y) 3 (A) for X and for Y 2 5 (B) for X and for Y 3 5 (C) for X and for Y 3 3 (D) for X and for Y 2 Q.12 The waveform shown in the figure is observed on the screen of a CRO. If the vertical attenuation is set to 0.5 V/div and horizontal scale is set to 2 s /div, then the peak-to-peak amplitude of the signal and the frequency of the signal are respectively 5 3 3 2 5 3 3 2

4 3 2

Volt

1 4

3

2

1

1

1 2 3 4

(A) 3 V, 8 MHz (B) 6 V, 250 kHz (C) 2 V, 4 kHz (D) 1.5 V, 125 kHz

Time

2

3

4

72

GATE ACADEMY®

GATE ACADEMY®

73

Cathode‐Ray Oscilloscope (CRO)

Answer Keys

Objective & Numerical Answer Type Questions 1.

C

2.

B

3.

A

4.

C

5.

C

6.

B

7.

B

8.

B

9.

D

10.

B

11.

C

12.

A

13.

A

14.

A

15.

A

16.

D

17.

B

18.

B

5.

B

Practice (Objective & Numerical Answer) Questions 1.

D

2.

D

3.

A

4.

A

6.

B

7.

C

8.

B

9.

C

Assignment (Objective & Numerical Answer) Questions 1.

D

2.

B

3.

B

4.

B

5.

A

6.

100

7.

B

8.

A

9.

C

10.

B

11.

D

12.

D 

Digital Volt Meter (DVM)

11

Formulas & Logics 1. Resolution :

Resolution :

R

1 in fraction 10 N

R

Vmax in volts 10 N

R

I max in Ampere 10 N

n  Number of full digits 2. Total error or Maximum Error

 [% Error due to reading  Reading value +

Objective & Numerical Ans Type Questions :

Q.1

Q.2

In a dual slope integrating type digital voltmeter the first integration is carried out for 10 periods of the supply frequency of 50 Hz. If the reference voltage used is 2V, the total conversion time for an input 1 V is sec [GATE-1992, IIT-Delhi] __________ The type of A/D converter normally used in a 3 1 2 digit multi meter is [GATE-1995, IIT-Kanpur]

(A) Dual - Slope integrating type (B) Voltage to frequency converter type

Number of counts  Full scale value Range of meter

Q.3

A 3 1 2 digit, 2 V full scale slope ADC has its integration time set to 300 ms. If the input to the ADC is (1  1sin 314t ) V, then the ADC output will be [GATE-1995, IIT-Kanpur]

Q.4

(A) 1.000

(B) 1.999

(C) 1.414

(D) 1.500

A 3

1

2

digit multi meter has an accuracy

specification of 0.5% of reading plus 5 counts. The value of an unknown resistance is red as 50.0  on the 200  scale of the meter, the value of the resistance is [GATE-2002, IISc-Bangalore]

(C) Flash (or parallel) type

(A) 50.0   0.25 

(B) 50.0   0.5 

(D) Successive approximation type

(C) 50.0   0.75 

(D) 50.0   100 

GATE ACADEMY®

Q.5

Q.6

75

A counter timer has a basic clock of 16 MHz. The count value displayed is in error by 1 count. The frequency at which (he error in the displayed value is the same whether the counter-timer is used in the frequency mode of operation or period mode of operation is [GATE-2002, IISc-Bangalore] (A) 16 MHz (B) 10 MHz (C) 8 MHz (D) 4 MHz The clock frequency of a timer-counter is 10 MHz. The timer-counter is used in the period mode and the input to the timercounter is a square wave of frequency 2 kHz. The display of the timer-counter will show a value [GATE-2003, IIT-Madras] (A) 200 (B) 2000 (C) 5000 (D) 50000

Digital Volt Meter (DVM)

. Common data Questions 4 to 5 .

In a dual slope ADC the reference voltage is 100 mV and the first integration is set as 50 ms. The input resistor of integrator is 100k and the integrating capacitor

0.047 F . Q.4

Q.5

Practice (objective & Num Ans) Questions :

Q.1

Q.2

Q.3

For an input voltage of 120 mV, the second integration (de-integration) period will be (A) 50 ms

(B) 60 ms

(C) 100 ms

(D) 120 ms

If the input of 120 mv, is corrupted by power supply interference at 50 Hz having peak amplitude of 3  mV, the worst-case error introduced by the interference in the reading is (A) 0 %

(B) 1 %

(C) 3 %

(D)  %

A 3 1 2 digit DVM has a lowest measuring range of 200 mV. Hence it can be concluded (A) Us best resolution is 0.1 in V (B) It’s poorest resolution is 0.2 m V (C) Its accuracy is at least 0.05% (D) The maximum voltage that can be measured in this range is 199.9m V A 3 1 2 digit digital multimeter can display

Assignment (objective & Num Ans) Questions :

(A) 999.5 (B) 5.999 (C) 555.5 (D) 1.999 Integrated output waveform for the dual slope ADC is shown in figure, the time T for an 8 bit counter with 4MHz clock will be V

Q.2

Q.1

(A) Is faster (B) Eliminates error due to drift (C) Can reduce error due to power supply (D) Does not require a stable voltage source

T (A) 0.032 ms (C) 0.64 ms

(B) 0.064 ms (D) 0.024

For a dual ADC type 3 1 2 digit DVM, the reference voltage is 100 mV and the first integration time is set to 300 ms. For some input voltage, the “deintegration” period is 370.2 ms. The DVM will indicate

Q.3

t

The advantage of a dual slop converter over successive approximation converter is that the dual slope converter

(A) 123.4

(B) 199.9

(C) 100.0

(D) 1.414

In a dual slope type digital voltmeter, an unknown signal voltage is integrated over 100 cycles of the clock. If the signal has a 50 Hz pick up, the maximum clock frequency can be (A) 50 Hz

(B) 5 KHz

(C) 10 KHz

(D) 50 KHz 3

1 2

Electrical & Electronic Measurements [Workbook]

GATE ACADEMY®

76

4 1 2 digit DMM has the error specification as: 0.2% of reading +10 counts. If a dc voltage of 100 V is read on its 200 V full scale, the maximum error that can be expected in the reading is (B) 0.2% (A) 0.1%

A

Q.4

(C) 0.3%

(D) 0.4%

Answer Keys

Objective & Numerical Answer Type Questions 1.

0.3

6.

C

2.

A

3.

A

4.

C

5.

A

5.

A

Practice (Objective & Numerical Answer) Questions 1.

D

2.

D

3.

B

4.

B

Assignment (Objective & Numerical Answer) Questions 1.

C

2.

A

3.

B

4.

C

