gate ee 2003 with solutions

GATE EE2003

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Q.1 - 30 Carry One Mark Each

MCQ 1.1 Figure Shows the waveform of the current passing through an inductor of resistance 1 Ω and inductance 2 H. The energy absorbed by the inductor in the first four seconds is

(A) 144 J (B) 98 J

(C) 132 J (D) 168 J

SOL 1.1 The Correct option is (C).Energy absorbed by the inductor coil is given as

EL Pdtt

0

= #

Where power P VI= I L dtdI= b l

So, EL LI dtdI dt

t

0

= b l#

For0 4t# # sec

EL 2 I dtdI dt

0

4

= b l#

EL 2 ( ) 2 ( )I dt I dt3 00

2

2

4

= +# # ,

,,dt

dI t

t

3 0 2

0 2 4< <

a # #=

=*

EL 6 .I dt0

2

= # =6(area under the curve ( )i t t− )

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6 2 621

# # #=

36= J Energy absorbed by 1 Ω resistor is

ER I Rdtt

2

0

= #

( ) ( )t dt dt3 1 62

0

22

2

4

#= +# # ,

A

I t t

t

3 0 2

6 2 4

# #

# #

==

)

9 36t33

0

2

2

4[ ]t#= +: D

24 72= + =96 JTotal energy absorbed in 4 sec E E EL R= + 36 96= + 132= J

MCQ 1.2 A segment of a circuit is shown in figure 5 , 4 2sinv V v tR c= = .The voltage vL is given by

(A) 3 8 cos t2− (B) 2sin t32

(C) sin t16 2 (D) 16 2cos t

SOL 1.2 The Correct option is (B).Applying KCL at center node



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iL 1 2iC= + + iL 3iC= +

iC C dtdvc=−

1 [4 2 ]sindtd t=−

8 2cos t=−so iL 8 2 3cos t=− + (current through inductor)Voltage across inductor

vL L dtdiL=

2 [3 8 2 ]cosdtd t#= −

32 2sin t=

MCQ 1.3 In the figure, 10 60 , 10 60 , 50 53.13 .Z Z Z1 2 3+ + += − = =% % % Thevenin impedance seen form X-Y is

(A) .56 66 45+ % (B) 60 30+ %

(C) 70 30+ % (D) .34 4 65+ %

SOL 1.3 Thevenin impedance can be obtain as following



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Zth ( || )Z Z Z3 1 2= +

given that Z1 10 60c+= − 10 j2

1 3= −c m

5(1 )j3= − Z2 10 60c+=

10 j2

1 3= +c m

5(1 )j3= + Z3 50 53.13c+=

50 j5

3 4= +b l

10(3 4 )j= +

So, Zth 10(3 4 )( ) ( )

( ) ( )j

j jj j

5 1 3 5 1 35 1 3 5 1 3= + +

− + +− +

10(3 4 )( )

j 1025 1 3= + + +

30 40 10j= + + 40 40j= + Zth 40 452 c+ Ω=Hence (A) is correct option.

MCQ 1.4 Two conductors are carrying forward and return current of +I and I− as shown in figure. The magnetic field intensity H at point P is

(A) dI Y

π (B)

dI X

π

(C) d

I Y2π

(D) d

I X2π

SOL 1.4 Due to the first conductor carrying I+ current, magnetic field intensity at point P is

H1 dI Y2π= (Direction is determined using right hand rule)

Similarly due to second conductor carrying I− current, magnetic field intensity is

H2 ( )dI Y2π= − −



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dI Y2π=

Total magnetic field intensity at point P. H H H1 2= +

dI

dIY Y2 2π π= +

dI Yπ=

Hence (A) is correct option.

MCQ 1.5 Two infinite strips of width w m in x -direction as shown in figure, are carrying forward and return currents of +I and I− in the z - direction. The strips are separated by distance of x m. The inductance per unit length of the configuration is measured to be L H/m. If the distance of separation between the strips in snow reduced to x/2 m, the inductance per unit length of the configuration is

(A) L2 H/m (B) /L 4 H/m

(C) /L 2 H/m (D) L4 H/m

SOL 1.5 The Correct option is ( ).

MCQ 1.6 A simple phase transformer has a maximum efficiency of 90% at full load and unity power factor. Efficiency at half load at the same power factor is(A) 86.7% (B) 88.26%

(C) 88.9% (D) 87.8%

SOL 1.6 Given that 1-φ transformer, maximum efficiency 90% at full load and unity power factorSo

η coscos

V I P PV I

i c2 2 2

2 2 2

φφ= + +

( . )

( . )cos

cosL F P P

L Fc2

2

i(Pu)φφ= + +

where . .L F is the load fator.At full load, load factor is



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. .L F 1PP

c

i= =

cos 2φ 1= at unity power factor

so, 90% P1 21 1

i

#= +

Pi .0 0555= MVA

At half load, load factor is

L.F .21 5= =

So,

η . . ( . ) .

.0 5 0 0555 0 5 0 0555

0 5 1 1002# #

##=

+ η . %87 8=Hence (D) is correct option.

MCQ 1.7 Group-I lists different applications and Group-II lists the motors for these applications. Match the application with the most suitable motor and choose the right combination among the choices given thereafter Group-I Group-II

P. Food mixer 1. Permanent magnet dc motor

Q. Cassette tape recorder 2. Single-phase induction motor

R. Domestic water pump 3. Universal motor

S. Escalator 4. Three-phase induction motor

5. DC series motor

6. Stepper motor

Codes:

P Q R S(A) 3 6 4 5(B) 1 3 2 4(C) 3 1 2 4(D) 3 2 1 4

SOL 1.7 In food mixer the universal motor is used and in cassette tap recorder permanent magnet DC motor is used. The Domestic water pump used the single and three phase induction motor and escalator used the three phase induction motor.Hence (C) is correct option.

MCQ 1.8 A stand alone engine driven synchronous generator is feeding a partly inductive load. A capacitor is now connected across the load to completely nullify the inductive current. For this operating condition.(A) the field current and fuel input have to be reduced



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(B) the field current and fuel input have to be increased

(C) the field current has to be increased and fuel input left unaltered

(D) the field current has to be reduced and fuel input left unaltered

SOL 1.8 Given a engine drive synchronous generator is feeding a partly inductive load. A capacitor is connected across the load to completely nullify the inductive current. Then the motor field current has to be reduced and fuel input left unaltered.Hence (D) is correct option.

MCQ 1.9 Curves X and Y in figure denote open circuit and full-load zero power factor(zpf) characteristics of a synchronous generator. Q is a point on the zpf characteristics at 1.0 p.u. voltage. The vertical distance PQ in figure gives the voltage drop across

(A) Synchronous reactance (B) Magnetizing reactance

(C) Potier reactance (D) Leakage reactance

SOL 1.9 The Correct option is (A).

Given open circuit and full-load zero power factor of a synchronous generator. At point Q the zero power factor at 1.0 pu voltage. The voltage drop at point PQ is across synchronous reactance.

MCQ 1.10 No-load test on a 3-phase induction motor was conducted at different supply voltage and a plot of input power versus voltage was drawn. This curve was extrapolated to intersect the y-axis. The intersection point yields(A) Core loss (B) Stator copper loss

(C) Stray load loss (D) Friction and windage loss

SOL 1.10 Given no load test on 3-φ induction motor, the graph between the input power and voltage drop is shown in figure, the intersection point yield the friction and windage loss.



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Hence (D) is correct option.

MCQ 1.11 Bundled conductors are mainly used in high voltage overhead transmission lines to(A) reduces transmission line losses

(B) increase mechanical strength of the line

(C) reduce corona

(D) reduce sag

SOL 1.11 The Correct option is (C).In case of bundled conductors, We know that self GMD of conductor is increased and in a conductor critical disruptive voltage of line depends upon GMD of conductor. Since GMD of conductor is increased this causes critical disruptive voltage is being reduced and if critical disruptive voltage is reduced, the corona loss will also be reduced.

MCQ 1.12 A power system consist of 300 buses out of which 20 buses are generator bus, 25 buses are the ones with reactive power support and 15 buses are the ones with fixed shunt capacitors. All the other buses are load buses. It is proposed to perform a load flow analysis in the system using Newton-Raphson method. The size of the Newton Raphson Jacobian matrix is(A) 553 553# (B) 540 540#

(C) 555 555# (D) 554 554#

SOL 1.12 The Correct option is (B). Given that no. of buses n 300= Generator bus 20= Reactive power support buses 25= Fixed buses with Shunt Capacitor 15= Slack buses (ns) 20 25 15 30= + − =a Size of Jacobian Matrix is given as 2( ) 2( )n n n ns s#= − − ( ) ( )2 300 30 2 300 30#= − − 540 540#=

MCQ 1.13 Choose two appropriate auxiliary components of a HVDC transmission system from the followingP. D.C line inductor



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Q. A.C line inductor

R. Reactive power sources

S. Distance relays on D.C line

T. Series capacitance on A.C. line

(A) P and Q (B) P and R

(C) Q and S (D) S and T

SOL 1.13 Auxiliary component in HVDC transmission system are DC line inductor and reactive power sources.Hence (B) is correct option.

MCQ 1.14 A round rotor generator with internal voltage .E 2 01 = pu and .X 1 1= pu is connected to a round rotor synchronous motor with internal voltage .E 1 32 = pu and 1.X 2= pu. The reactance of the line connecting the generator to the motor is 0.5 pu. When the generator supplies 0.5 pu power, the rotor angle difference between the machines will be(A) 57.42c (B) 1c

(C) 32.58c (D) 122.58c

SOL 1.14 The Correct option is (C).a Exchanged electrical power is being given as follows

P ( )sinXEV

d1 2δ δ= −6 @ ...(1)

Given that P sPower upply by generator" 0.5= pu E Voltage for rotar generator" 2.0= pu V Voltage of motor rotor" 1.3= pu Xd X Reactance of generator Reactance of motoreq= = + Recatance of connecting line+ Xd 1.1 1.2 .5 2.80= + + = 1 2δ δ− Rotor angle difference ?= =

from eq(1), .0 5 .. ( )sin2 8

2 1 31 2

# δ δ= −

1 2& δ δ− .. .sin 2 6

2 8 0 51 #= −b l

1 2& δ δ− .32 58=

MCQ 1.15 The interrupting time of a circuit breaker is the period between the instant of(A) initiation of short circuit and the arc extinction on an opening operation

(B) energizing of the trip circuit and the arc extinction on an opening operation

(C) initiation of short circuit and the parting of primary arc contacts

(D) energizing of the trip circuit and the parting of primary arc contacts

SOL 1.15 Time period between energization of trip circuit and the arc extinction on an



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opening operation is known as the interrupting time of Circuit breaker.Hence (B) is correct option.

MCQ 1.16 The variation of drain current with gate-to-source voltage (I VD GS− characteristic) of a MOSFET is shown in figure. The MOSFET is

(A) an n-channel depletion mode device

(B) an n-channel enhancement mode device

(C) an p-channel depletion mode device

(D) an p-channel enhancement mode device

SOL 1.16 Since there exists a drain current for zero gate voltage ( )V 0GS = , so it is a depletion mode device.ID increases for negative values of gate voltages so it is a p-type depletion mode device.Hence (C) is correct option.

MCQ 1.17 In the circuit of figure, assume that the transistor has 99hfe = and .V 0 7BE = V. The value of collector current IC of the transistor is approximately

(A) [3.3/3.3] mA (B) [3.3/(3.3+3.3)] mA

(C) [3.3/.33] mA (D) [3.3(33+3.3)] mA

SOL 1.17 The Correct option is (B).Applying KVL in input loop,

( ) ( . )

4 (33 10 ) 0.7 (3.3 10 )( 1) 0

I V I

I h I

4 33 10 3 3 10 0B BE E

B fe B

3 3

3 3

# #

# #

− − − =

− − − + =

( 1)I h IE fe Ba = +

3.3 ( ) ( . )( ) I33 10 3 3 10 99 1 B3 3# #= + +6 @



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IB ..

33 10 3 3 10 1003 3

3 3# # #=

+ IC h Ife B=

IC [ . . ]

.0 33 3 3 100

99 3 3 mA#

#=+

IC . .

.0 33 3 3

3 3 mA=+

MCQ 1.18 For the circuit of figure with an ideal operational amplifier, the maximum phase shift of the output vout with reference to the input vin is

(A) 0c (B) 90c−

(C) 90c+ (D) 180! c

SOL 1.18 Let the voltages at positive and negative terminals of op-amp are v vand+ - respectively. Then by applying nodal equations.

R

v vR

v vin out

1 1

− + −- - 0=

2 v-- v vin out= + ..(1)

Similarly,

R

v v

j C

v1

0in

ω

− + −+ +

c m

0=

( )v v v j CRin ω− ++ + 0=

(1 )v j CRω++ Vin= ..(2)

By equation (1) & (2)

j CRv

12 in

ω+ v vin out= + v va =+ -" (ideal op-amp)

vj CR12 1in ω+

−; E vout=

vout ( )

vj CRj CR

11

in ωω=

+−

Phase shift in output is given by θ ( ) ( )tan tanCR CR1 1ω ω= − −- -



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θ ( ) ( )tan tanCR CR1 1π ω ω= − −- -

θ 2 ( )tan CR1π ω= − -

Maximum phase shift θ π=Hence (D) is correct option.

MCQ 1.19 Figure shows a 4 to 1 MUX to be used to implement the sum S of a 1-bit full adder with input bits P and Q and the carry input Cin . Which of the following combinations of inputs to , ,I I I0 1 2 and I3 of the MUX will realize the sum S ?

(A) ;I I C I I Cin in0 1 2 3= = = = (B) ;I I C I I Cin in0 1 2 3= = = =

(C) ;I I C I I Cin in0 3 1 2= = = = (D) ;I I C I I Cin in0 3 1 2= = = =

SOL 1.19 In given circuit MUX implements a 1-bit full adder, so output of MUX is given by. F Sum A Q Cin5 5==Truth table can be obtain as.

P Q Cin Sum

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0

1 1 1 1Sum is. Sum P Q C PQC P Q C P QCin in in in= + + +Output of MUX can be written as F P Q I PQ I PQ I PQ I0 1 2 3$ $ $ $= + + +Inputs are, I0 , , ,C I C I C I Cin in in in1 2 3= = = =Hence (C) is correct option.

MCQ 1.20 When a program is being executed in an 8085 microprocessor, its Program Counter contains



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(A) the number of instructions in the current program that have already been executed

(B) the total number of instructions in the program being executed.

(C) the memory address of the instruction that is being currently executed

(D) the memory address of the instruction that is to be executed next

SOL 1.20 Program counter contains address of the instruction that is to be executed next.Hence (D) is correct option.

MCQ 1.21 A control system is defined by the following mathematical relationship

( )dtd x

dtdx x e6 5 12 1 t

2

22+ + = − -

The response of the system as t " 3 is(A) x 6= (B) x 2=

(C) .x 2 4= (D) x 2=−

SOL 1.21 Given system equation is.

6 5dtd x

dtdx x2

2

+ + ( )e12 1 t2= − −

Taking Laplace transform on both side.

( ) ( ) ( )s X s sX s X s6 52 + + 12 s s1

21= − +: D

( ) ( )s s X s6 52 + + 12( 2)

2s s

= +; E

System transfer function is

( )X s ( )( )( )s s s s2 5 1

24= + + +

Response of the system as t " 3 is given by ( )lim f t

t"3 lim ( )sF s

s 0=

" (final value theorem)

( 2)( 5)( 1)

24lim ss s s ss 0

= + + +"; E

2 524#

=

.2 4=Hence (C) is correct option.

MCQ 1.22 A lead compensator used for a closed loop controller has the following transfer function

(1 )(1 )K

bsas

++

For such a lead compensator(A) a b< (B) b a<



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(C) a Kb> (D) a Kb<

SOL 1.22 Transfer function of lead compensator is given by.

( )H s

bs

K as

1

1=

+

+

a

a

k

k

( )H jω Kj b

j a

1

1

ω

ω

=+

+

a

a

k

kR

T

SSSS

V

X

WWWW

So, phase response of the compensator is.

( )hθ ω tan tana b1 1ω ω= −− −a ak k

1

tan

ab

a b2

1

ω

ω ω=

+

−−

J

L

KKK

N

P

OOO

( )tan

abb a1

2ωω=

+−−

; E

hθ should be positive for phase lead compensation

So, ( )hθ ω ( )

0tanab

b a >12ω

ω=+−−

; E

a b<Hence (A) is correct option

MCQ 1.23 A second order system starts with an initial condition of 23= G without any external

input. The state transition matrix for the system is given by e

e00t

t

2-

-= G. The state of the system at the end of 1 second is given by

(A) ..

0 2711 100= G (B)

.

.0 1350 368= G

(C) ..

0 2710 736= G (D)

.

.0 1351 100= G

SOL 1.23 Since there is no external input, so state is given by ( )tX ( ) (0)t Xφ=

( )t "φ state transition matrix[0]X "initial condition

So ( )x t e

e00 2

3

t

t

2

=−

−> >H H

( )x t ee

23

t

t

2

=−

−> H

At t 1= , state of the system

( )x tt 1=

ee

22

2

1=−

−> H ..

0 2711 100= > H



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Hence (A) is correct option

MCQ 1.24 A Manganin swap resistance is connected in series with a moving coil ammeter consisting of a milli-ammeter and a suitable shunt in order to(A) minimise the effect of temperature variation

(B) obtain large deflecting torque

(C) reduce the size of the meter

(D) minimise the effect of stray magnetic fields

SOL 1.24 In PMCC instruments, as temperature increases the coil resistance increases. Swamp resistors are connected in series with the moving coil to provide temperature compensation. Swamping resistors is made of Manganin, which has a zero-temperature coefficient.


MCQ 1.25 The effect of stray magnetic field on the actuating torque of a portable instrument is maximum when the operating field of the instrument and the stray fields are(A) perpendicular (B) parallel

(C) inclined at 60% (D) inclined at 30%

SOL 1.25 The Correct option is (B).Effect of stray magnetic field is maximum when the operating field and stray fields are parallel.

MCQ 1.26 A reading of 120 is obtained when standard inductor was connected in the circuit of a Q-meter and the variable capacitor is adjusted to value of 300 pF. A lossless capacitor of 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(A) 100 (B) 200

(C) 300 (D) 500

SOL 1.26 The Correct option is (A).Let C1 300= pF

Q C R120 11ω= =

Now when Cx is connected in parallel with variable resistor 'C 2001 = pF



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Q ( ' )C C R

120 1x1ω= = +

So C1 'C Cx1= + 300 C200 x= + Cx 100= pF

MCQ 1.27 Figure shows a thyristor with the standard terminations of anode (A), cathode (K), gate (G) and the different junctions named J1, J2 and J3. When the thyristor is turned on and conducting

(A) J1 and J2 are forward biased and J3 is reverse biased

(B) J1 and J3 are forward biased and J2 is reverse biased

(C) J1 is forward biased and J2 and J3 are reverse biased

(D) J1, J2 and J3 are all forward biased

SOL 1.27 When thyristor turned on at that time J2 junction will break. So J1, J2, J3 all are in forward bias.Hence (D) is correct option.

MCQ 1.28 Figure shows a MOSFET with an integral body diode. It is employed as a power switching device in the ON and OFF states through appropriate control. The ON and OFF states of the switch are given on the V IDS S− plane by



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SOL 1.28 The ON-OFF state of switch is given on V IDS S− plane as following

When V veDS =+ , diode conducts and I 0S = V veDS =− , diode opens, but I 0S = , D ve"− potential.Hence (D) is correct option.

MCQ 1.29 The speed/torque regimes in a dc motor and the control methods suitable for the same are given respectively in List-II and List-I List-I List-IIP. Field Control 1. Below base speedQ. Armature Control 2. Above base speed 3. Above base torque 4. Below base torqueCodes:(A) P-1, Q-3 (B) P-2, Q-1

(C) P-2, Q-3 (D) P-1, Q-4

SOL 1.29 The Correct option is (B).P. Field control-Above base speedQ. Armature control-below base torque

MCQ 1.30 A fully controlled natural commutated 3-phase bridge rectifier is operating with a firing angle 30cα = , The peak to peak voltage ripple expressed as a ratio of the peak output dc voltage at the output of the converter bridge is(A) 0.5 (B) /3 2

(C) 123−c m (D) 3 1−

SOL 1.30 The Correct option is (A).As we know in fully controlled rectifier. VPP ( / )cosV V 6m m π α= − + 30a cα =or VPP [1 ( /6 30 )]cosVm cπ= − +



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or VV

m

PP .0 5=

Q. 31 - 90 carry two marks each

MCQ 1.31 In the circuit of figure, the magnitudes of VL and VC are twice that of VR . Given that 50f Hz= , the inductance of the coil is

(A) 2.14 mH (B) 5.30 H

(C) 31.8 mH (D) 1.32 H

SOL 1.31 Given that magnitudes of VL and VC are twice of VR

VL VC= 2VR= (Circuit is at resonance)Voltage across inductor VL i j LR # ω=Current iR at resonance

iR R5 0+=

%

55= 1 A=

so, VL Lω= 2VR= Lω 2 5#= 5VR = V, at resonance 2 50 L# # #π 10=

L 31410= 31.8= mH

Hence (C) is correct option.

MCQ 1.32 In figure, the potential difference between points P and Q is

(A) 12 V (B) 10 V



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(C) 6 V− (D) 8 V

SOL 1.32 The Correct option is (C).Applying nodal analysis in the circuitAt node P

2 V V2

108

P P+ − + 0=

16 4 40V VP P+ − + 0= 5 24VP − 0=

& VP 524= Volt

At node Q

2 V V

410

60Q Q= − + −

24 3 30 2V VQ Q= − + 5 54VQ − 0=

& VQ 554= V

Potential difference between P-Q VPQ V VP Q= −

524

554= − 6=− V

MCQ 1.33 Two ac sources feed a common variable resistive load as shown in figure. Under the maximum power transfer condition, the power absorbed by the load resistance RL is

(A) 2200 W (B) 1250 W

(C) 1000 W (D) 625 W

SOL 1.33 First obtain equivalent Thevenin circuit across load RL

Thevenin voltage



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jV

jV

6 8110 0

6 890 0th thc c+ +

+− + +

− 0=

2 200 0Vth c+− 0=& Vth 100 0c+= V Thevenin impedance

Zth (6 8 ) || (6 8 )j jΩ Ω= + + (3 4 )j Ω= +For maximum power transfer RL Zth= 3 42 2= + 5 Ω=

Power in load P i Reff L

2=

P 5j3 4 5100 2

#= + +

( )

580100 2

#= 625= WattHence (D) is correct option.

MCQ 1.34 In figure, the value of R is

(A) 10 Ω (B) 18 Ω

(C) 24 Ω (D) 12 Ω

SOL 1.34 By applying mesh analysis in the circuit



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10I1 = A, 5I2 =− ACurrent in 2 Ω resistor I2Ω ( )I I1 2= − − 10 ( 5)= − − 15= ASo, voltage VA 15 2 30#= = VoltNow we can easily find out current in all branches as following

Current in resistor R is 5 A

5 R100 40= −

R 560= 12 Ω=


MCQ 1.35 A balanced delta connected load of (8 6)j Ω+ per phase is connected to a 400 V, 50 Hz, 3-phase supply lines. If the input power factor is to be improved to 0.9 by connecting a bank of star connected capacitor the required kVAR of the of the bank is(A) 42.7 (B) 10.2

(C) 28.8 (D) 38.4

SOL 1.35 The Correct option is (B).Given data A balanced delta connected load j8 6 2= + = V2 400= volt Improved Power Factor cos 2φ .90= 1φ 6/8 36.85tan 1 c= =−

^ h



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2φ ( .9) 25.84cos 01 c= =−

I .

40 36.86ZV

j8 6400

10 36 86400

cc

++= = + = = −

I j32 24= −Since Power factor is Improved by connecting a Y-connected capacitor bank like as

Phasor diagram is being given by as follows

In figure oa cos cosI I2 1φ φ= =l

.cosI 25 84cl 32= .I 0 9#l 32= Il .35 55= ac 24= Amp. ( )sinIac 1φ= ab 35.55 25.84sin sinI 2 cφ= =l

ab .15 49= Amp Ic bc ac ab 24 15.49 8.51= = − = − = Amp

KVAR of Capacitor bank V I1000

3 C# #=

.1000

3 400 8 51# #=

.10 2= KVAR

MCQ 1.36 In the circuit shown in figure, the switch S is closed at time (t = 0). The voltage across the inductance at t 0= +, is



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(A) 2 V (B) 4 V

(C) 6− V (D) 8 V

SOL 1.36 Before 0t = , the switch was opened so current in inductor and voltage across capacitor for 0t < is zero

(0 ) 0vc =− , ( )i 0 0L =-

at 0t = , when the switch is closed, inductor current and capacitor voltage does not change simultaneously so

(0 ) (0 ) 0v vc c= =+ − , (0 ) (0 ) 0i iL L= =+ −

At 0t = + the circuit is

Simplified circuit

Voltage across inductor (at 0t = +)

(0 )vL+ 23 2

10#= + 4= Volt

Hence (B) is correct option.

MCQ 1.37 The h-parameters for a two-port network are defined by

EI

hh

hh

IE

1

2

11

21

12

22

1

2== = =G G G

For the two-port network shown in figure, the value of h12 is given by

(A) 0.125 (B) 0.167

(C) 0.625 (D) 0.25



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SOL 1.37 The Correct option is (D).Given that E1 h I h E11 1 12 2= +and I2 h I h E21 1 22 2= +Parameter h12 is given as

h12 EE

( )open circuitI2

1

01

==

At node A

E E E E E2 2 4

A A A1 2− + − + 0=

E5 A E E2 21 2= + ...(1)Similarly

E E E2 2

A1 1− + 0=

2E1 EA= ...(2)From (1) and (2) 5(2 )E1 2 2E E1 2= + 8E1 2E2=

h12 EE

2

1= 41=

MCQ 1.38 A point charge of +I nC is placed in a space with permittivity of .8 85 10 12#- F/m

as shown in figure. The potential difference VPQ between two points P and Q at

distance of 40 mm and 20 mm respectively fr0m the point charge is

(A) 0.22 kV (B) 225− V

(C) .2 24− kV (D) 15 V

SOL 1.38 The Correct option is (B). VPQ V VP Q= −

KQ KQOP OQ= −

40 10

9 10 1 1020 10

9 10 1 103

9 9

3

9 9

#

# # #

#

# # #= −−

−

−

−



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9 10 401

2013

#= −: D 225=− Volt

MCQ 1.39 A parallel plate capacitor has an electrode area of 100 mm2, with spacing of 0.1 mm between the electrodes. The dielectric between the plates is air with a permittivity of .8 85 10 12#

- F/m. The charge on the capacitor is 100 V. The stored energy in the capacitor is(A) 8.85 pJ (B) 440 pJ

(C) 22.1 nJ (D) 44.3 nJ

SOL 1.39 The Correct option is (D).Energy stored in Capacitor is

E CV21 2=

C dA0ε=

.

.0 1 10

8 85 10 100 103

12 6

#

# # #= −

− −

.8 85 10 12#= − F

E . ( )21 8 85 10 10012 2# # #= −

.44 3= nJ

MCQ 1.40 A composite parallel plate capacitor is made up of two different dielectric material with different thickness (t1 and t2) as shown in figure. The two different dielectric materials are separated by a conducting foil F. The voltage of the conducting foil is

(A) 52 V (B) 60 V

(C) 67 V (D) 33 V

SOL 1.40 The figure is as shown below

The Capacitor shown in Figure is made up of two capacitor C1 and C2 connected in series.



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C1 ,tA C t

Ar r

1

0 12

2

0 2ε ε ε ε= =

Since C1 and C2 are in series charge on both capacitor is same. Q1 Q2= ( )C V1001 − C V2= (Let V is the voltage of foil)

( )tA V100r

1

0 1ε ε − tAVr

2

0 2ε ε=

. ( )V0 53 100 − V1

4=

V300 3− V2= 300 5 60V V&= = VoltHence (B) is correct option.

MCQ 1.41 Figure shows an ideal single-phase transformer. The primary and secondary coils are wound on the core as shown. Turns ratio /N N 21 2 = .The correct phasors of voltages ,E E1 2, currents ,I I1 2 and core flux Φ are as shown in

SOL 1.41 Correct Option is ( )

MCQ 1.42 To conduct load test on a dc shunt motor, it is coupled to a generator which is identical to the motor. The field of the generator is also connected to the same supply source as the motor. The armature of generator is connected to a load resistance. The armature resistance is 0.02 p.u. Armature reaction and mechanical losses can be neglected. With rated voltage across the motor, the load resistance



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across the generator is adjusted to obtain rated armature current in both motor and generator. The p.u value of this load resistance is(A) 1.0 (B) 0.98

(C) 0.96 (D) 0.94

SOL 1.42 Hence (C) is correct option.

Given that:The armature resistance in per unit is 0.2so, Ra .0 2=back emf equation of motor is Eb V I Ra a= −given that no mechanical losses and armature reaction is neglected, so per unit value of emf induced by motor is Eb .0 98=The DC shunt motor is mechanically coupled by the generator so the emf induced by motor and generator is equal Eg Eb=so voltage generated by the generator is V . . .0 98 1 0 2 0 96#= − =per unit value of load resistance is equal to 0.96

MCQ 1.43 Figure shows a Y3− connected, 3-phase distribution transformer used to step down the voltage from 11000 V to 415 V line-to-line. It has two switches S1 and S2. Under normal conditions S1 is closed and S2 is open. Under certain special conditions S1 is open and S2 is closed. In such a case the magnitude of the voltage across the LV terminals a and c is

(A) 240 V (B) 480 V

(C) 415 V (D) 0 V



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SOL 1.43 Given that when the switch S1 is closed and S2 is open then the 11000 V is step down at 415 V outputSecond time when the switch S1 is open and switch S2 is closed then 2-phase supply is connected to the transformer then the ratio of voltage is

VV

2

1 26.50NN

41511000

2

1= = =

The output terminal a and c are in opposite phase so cancelled with each other and terminal is equal to zero volt.Hence (D) is correct option.

MCQ 1.44 Figure shows an ideal three-winding transformer. The three windings 1, 2, 3 of the transformer are wound on the same core as shown. The turns ratio : :N N N1 2 3 is 4:2:1. A resistor of 10 Ω is connected across winding-2. A capacitor of reactance 2.5 Ω is connected across winding-3. Winding-1 is connected across a 400 V, ac supply. If the supply voltage phasor 400 0V1 += %, the supply current phasor I1 is given by

(A) ( 10 10)j− + A (B) ( 10 10)j− − A

(C) (10 10)j+ A (D) (10 10)j− A

SOL 1.44 Given that N1: :N N2 3 is : :4 2 1Resistance R 10 Ω= V1 400 V=so,

VV

2

1 NN

24

2

1= =

V2 V4

2 1=

200 V=and

VV

3

1 NN

14

3

1= =

V3 100 V=so current in secondary winding

I2 RV

102002= =



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I2 20 A=The current in third winding when the capacitor is connectedso

I3 .jXV

j j2 5100 40

c

3= − = − =

When the secondary winding current I2 is referred to primary side i.e I '1

So

II '

2

1 NN

42

1

2= =

I '1

20 102 A= =

and winding third current I3 is referred to Primary side i.e I ''1. I3 flows to opposite

to I1 So

II ''

3

1

− NN

41

1

3= =

I ''1 j10=−

So total current in primary winding is I1 I I'' ''

1 2= + 10 10j A= −Hence (D) is correct option.

MCQ 1.45 Following are some of the properties of rotating electrical machinesP. Stator winding current is dc, rotor winding current is ac.Q. Stator winding current is ac, rotor winding current is dc.R. Stator winding current is ac, rotor winding current is ac.S. Stator has salient poles and rotor has commutator.T. Rotor has salient poles and sliprings and stator is cylindrical.U. Both stator and rotor have poly-phase windings.DC machines, Synchronous machines and Induction machines exhibit some of the above properties as given in the following table.Indicate the correct combination from this table

DCMachine

Synchronous Machines

InductionMachines

(A) P,S (B) Q,U(C) P,S(D) R,S

Q,TP,TR,UQ,U

R,UR,SQ,TP,T

SOL 1.45 The Correct option is (A).Given that:P Stator winding current is dc, rotor winding current is ac



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Q Stator winding current is ac, rotor winding current is dc

R Stator winding current is ac, rotor winding current is ac

S Stator has salient pole and rotor has commutator

T Rotor has salient pole and slip rings and stator is cylindrical

U Both stator and rotor have poly-phase windings

SoDC motor/machines:The stator winding is connected to dc supply and rotor winding flows ac current. Stator is made of salient pole and Commutator is connected to the rotor so rotor winding is supply ac power.

Induction machines:In induction motor the ac supply is connected to stator winding and rotor and stator are made of poly-phase windings.

Synchronous machines:In this type machines the stator is connected to ac supply but rotor winding is excited by dc supply. The rotor is made of both salient pole and slip rings and stator is made of cylindrical.

MCQ 1.46 When stator and rotor windings of a 2-pole rotating electrical machine are excited, each would produce a sinusoidal mmf distribution in the airgap with peal values Fs and Fr respectively. The rotor mmf lags stator mmf by a space angle δ at any instant as shown in figure. Thus, half of stator and rotor surfaces will form one pole with the other half forming the second pole. Further, the direction of torque acting on the rotor can be clockwise or counter-clockwise.

The following table gives four set of statement as regards poles and torque. Select the correct set corresponding to the mmf axes as shown in figure.

StatorSurface

ABC forms

StatorSurface

CDA forms

RotorSurface

abc forms

Rotorsurface

cda forms

Torqueis



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(A) North Pole(B) South Pole

(C) North Pole

(D) South Pole

South PoleNorth Pole

South Pole

North Pole

North PoleNorth Pole

South Pole

South Pole

South PoleSouth Pole

North Pole

North Pole

ClockwiseCounter

ClockwiseCounter

ClockwiseClockwise

SOL 1.46 Given thatFs is the peak value of stator mmf axis. Fr is the peak value of rotor mmf axis. The rotor mmf lags stator mmf by space angleδ. The direction of torque acting on the rotor is clockwise or counter clockwise.When the opposite pole is produced in same half portion of stator and rotor then the rotor moves. So portion of stator is north-pole in ABC and rotor abc is produced south pole as well as portion surface CDA is produced south pole and the rotor cda is produced North pole.The torque direction of the rotor is clock wise and torque at surface is in counter clockwise direction.Hence (C) is correct option.

MCQ 1.47 A 4-pole, 3-phase, double-layer winding is housed in a 36-slot stator for an ac machine with 60c phase spread. Coil span is 7 short pitches. Number of slots in which top and bottom layers belong to different phases is(A) 24 (B) 18

(C) 12 (D) 0

SOL 1.47 Given that:A 4-pole, 3-φ, double layer winding has 36 slots stator with 60c phase spread, coil span is 7 short pitchedso,

Pole pitch poleslot=

436 9= =

Slot/pole/phase 3=so,3-slots in one phase, if it is chorded by 2 slots then Out of 3 2" have different phase Out of 36 24" have different phase.Hence (A) is correct option.

MCQ 1.48 A 3-phase induction motor is driving a constant torque load at rated voltage and frequency. If both voltage and frequency are halved, following statements relate to the new condition if stator resistance, leakage reactance and core loss are ignored1. The difference between synchronous speed and actual speed remains same



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2. The airgap flux remains same

3. The stator current remains same

4. The p.u. slip remains same

Among the above, current statements are

(A) All (B) 1, 2 and 3

(C) 2, 3 and 4 (D) 1 and 4

SOL 1.48 Given that:3-φ induction motor is driving a constant load torque at rated voltage and frequency. Voltage and frequency are halved and stator resistance, leakage reactance and core losses are ignored.Then the motor synchronous speed and actual speed difference are same.

Ns Pf120=

The leakage reactance are ignored then the air gap flux remains same and the stator resistance are ignored then the stator current remain same.Hence (B) is correct option.

MCQ 1.49 A single-phase induction motor with only the main winding excited would exhibit the following response at synchronous speed(A) Rotor current is zero

(B) Rotor current is non-zero and is at slip frequency

(C) Forward and backward rotaling fields are equal

(D) Forward rotating field is more than the backward rotating field

SOL 1.49 Given that:1-φ induction motor main winding excited then the rotating field of motor changes, the forward rotating field of motor is greater then the back ward rotating field.Hence (D) is correct option.

MCQ 1.50 A dc series motor driving and electric train faces a constant power load. It is running at rated speed and rated voltage. If the speed has to be brought down to 0.25 p.u. the supply voltage has to be approximately brought down to(A) 0.75 p.u (B) 0.5 p.u

(C) 0.25 p.u (D) 0.125 p.u

SOL 1.50 Given that:A dc series motor driving a constant power load running at rated speed and rated voltage. It’s speed brought down 0.25 pu. ThenEmf equation of dc series motor E ( )V R Ra se= − + R Ra se+ R=



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so, E V IR= − K Nφ=

then N KEφ=

In series motor Iφα

so, N KIV IR= −

At constant power load E I# T W Const#= = ...(1) T K I KI 2φ= = ...(2)If W is decreased then torque increases to maintain power constant. T I 2

\

W 41= then T 4=

So current is increased 2 time and voltage brought down to 0.5 pu.Hence (B) is correct option.

MCQ 1.51 The ABCD parameters of a 3-phase overhead transmission line are 0.9 0 , 200 90A D Bc c+ + Ω= = = and 0.95 10 90C S3# += %- . At no-load condition

a shunt inductive, reactor is connected at the receiving end of the line to limit the receiving-end voltage to be equal to the sending-end voltage. The ohmic value of the reactor is (A) 3 Ω (B) 2000 Ω

(C) 105.26 Ω (D) 1052.6 Ω

SOL 1.51 The Correct option is (B).Given that ABCD parameters of line as 0.9 0A D c+= = , 200 90B + Ω= % , 0.95 10 90C S3# += %- .at no-load condition, Receiving end voltage( )VR sending end voltage(V )S= ohmic value of reactor ?=We know VS AV BIR R= + a VS VR= VR AV BIR R= + (1 )V AR − BIR=

IV

R

R AB

1= −

.1 0 9 0

200 90cc

++= −

IV

R

R 200 900 c+=

The ohmic value of reactor 2000 Ω=



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MCQ 1.52 A surge of 20 kV magnitude travels along a lossless cable towards its junction with two identical lossless overhead transmission lines. The inductance and the capacitance of the cable are 0.4 mH and 0.5 Fμ per km. The inductance and capacitance of the overhead transmission lines are 1.5 mH and 0.015 Fμ per km. The magnitude of the voltage at the junction due to surge is(A) 36.72 kV (B) 18.36 kV

(C) 6.07 kV (D) 33.93 kV

SOL 1.52 The Correct option is (A).Surge impedance of cable

Z1 CL= ; .L 0 4= mH/km, 0.5C Fμ= /km

.. 28.284

0 5 100 4 10

6

3

#

#= =−

−

surge impedance of overhead transmission line

Z2 Z CL

3= = ; .L 1 5= mm/km, 0.015C F/kmμ=

Z Z2 3= .. 316.23

0 015 101 5 10

6

5

#

#= =−

−

Now the magnitude of voltage at junction due to surge is being given by as

Vl Z ZV Z2

2 1

2# #= + V 20= kV

..

316 28 2842 20 10 316 233# # #= +

.36 72= kV

MCQ 1.53 A dc distribution system is shown in figure with load current as marked. The two ends of the feeder are fed by voltage sources such that 3V VP Q− = V. The value of the voltage VP for a minimum voltage of 220 V at any point along the feeder is

(A) 225.89 V (B) 222.89 V

(C) 220.0 V (D) 228.58 V

SOL 1.53 Let that current in line is I amp thanfrom figure current in line section PR is ( 10)I − ampcurrent in line section RS is ( 10 20) ( 30)I I− − = − ampcurrent in SQ Section is ( ) ( )I I30 30 60− − = − amp



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Given that VP and VQ are such that

V VP Q− 3 V=

by applying KVL through whole line V VP Q− ( 10)0.1 ( 30)0.15 ( 60) .2I I I 0#= − + − + −

3& .45 17.5I0= −

I .. 45.550 45

20 5= = amp

Now the line drop is being given as ( 10) .1 ( 30) .15 ( 60) .2I I I0 0 0= − + − + − (33.55)0.1 (15.55)0.15 (14.45)0.2= + + .8 58= VThe value of VP for minimum voltage of 220 V at any feeder is 220 Line voltage= + 220 8.58= + 228.58= VHence (D) is correct option.

MCQ 1.54 A 3-phase 11 kV generator feeds power to a constant power unity power factor load of 100 MW through a 3-phase transmission line. The line-to line voltage at the terminals of the machine is maintained constant at 11 kV. The per unit positive sequence impedance of the line based on 100 MVA and 11 kV is 0.2j . The line to line voltage at the load terminals is measured to be less than 11 kV. The total reactive power to be injected at the terminals of the load to increase the line-to-line voltage at the load terminals to 11 kV is(A) 100 MVAR (B) 10.1 MVAR

(C) 100− MVAR (D) .10 1− MVAR

SOL 1.54 The Correct option is (D). Given Load Power 100= MW V VS R= 11= kV

Impedance of line ZL MVp.u. (kV)2

#=

. ( )j

1000 2 11 2

#= .242j0 Ω=

We know PL sin

XV VS R δ

=

100 106# . sin0 242

11 10 11 103 3# # # δ=

.121

100 0 242# sin δ=



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δ (0.2) 11.537sin 1 c= =−

Reactive Power is being given by

QL cosXV V

XVS R R

2

δ= −

. (11.537 ) .( )

cos0 24211 10 11 10

0 24211 103 3 3 2

# # # #c= −

. [ (11.537 ) 1]cos0 242121 106

# c= −

.10 1=− MVAR

MCQ 1.55 The bus impedance matrix of a 4-bus power system is given by

Zbus

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

jjjj

jjjj

jjjj

jjjj

0 34350 28600 27230 2277

0 28600 34080 25860 2414

0 27230 25860 27910 2209

0 22770 24140 22090 2791

=

R

T

SSSSS

V

X

WWWWW

A branch having an impedance of 0.2j Ω is connected betweenbus 2 and the reference. Then the values of Z22,new and Z23,new of the bus impedance matrix of the modified network are respectively(A) .j0 5408 Ω and .j0 4586 Ω

(B) 0.j 1260 Ω and .j0 0956 Ω

(C) .j0 5408 Ω and .j0 0956 Ω

(D) 0.j 1260 Ω and 0.1j 630 Ω

SOL 1.55 The Correct option is (B).Given the bus Impedance Matrix of a 4-bus Power System

Zbus

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

jjjj

jjjj

jjjj

jjjj

0 34350 28600 27230 2277

0 28600 34080 25860 2414

0 27230 25860 27910 2209

0 22770 24140 22090 2791

=

R

T

SSSSSS

V

X

WWWWWW

Now a branch os .j0 2 Ω is connected between bus 2 and reference

ZB(New) Z Z Z

Z

ZZ Z1

(Bij b

ij

nj

ji jnOld) h g= − +

R

T

SSSS

8

V

X

WWWW

B

New element 0.2Z jb Ω= is connected in jth and reference bus2j = , n 4= so

Z Z

ZZZZ

Z Z Z Z1ij b

12

22

23

24

21 22 23 24+

R

T

SSSSSS

8

V

X

WWWWWW

B



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( . ) .

.

.

.

.

. . . .j j

jjjj

j j j j0 3408 0 2

1

0 28600 34080 25860 2414

0 2860 0 3408 0 2586 0 2414= +

R

T

SSSSSS

68

V

X

WWWWWW

@B ...(1)

Given that we are required to change only ,Z Z22 23

So in equation (1) Z 22l ( . )( . )

.2147j

jj

0 54080 3408

02 2

= =

Z 23l .( . )( . )

.16296j

j0 54080 3408 0 2586

02

= =

Z22( )New Z Z22( ) 22Old= − l .3408 .2147 .1260j j j0 0 0= − = Z23( )New Z Z23 23(Old)= − l 0.2586 0.16296 0.0956j j j= − =

MCQ 1.56 A 20-MVA, 6.6-kV, 3-phase alternator is connected to a 3-phase transmission line. The per unit positive-sequence, negative-sequence and zero-sequence impedances of the alternator are .1j0 , .1j0 and 0.j 04 respectively. The neutral of the alternator is connected to ground through an inductive reactor of 0.j 05 p.u. The per unit positive-, negative- and zero-sequence impedances of transmission line are

.1j0 , .1j0 and 0.j 3, respectively. All per unit values are based on the machine ratings. A solid ground fault occurs at one phase of the far end of the transmission line. The voltage of the alternator neutral with respect to ground during the fault is(A) 513.8 V (B) 889.9 V

(C) 1112.0 V (D) 642.2 V

SOL 1.56 Total zero sequence impedance, ve+ sequence impedance and ve− sequence impedances Z0 ( ) ( ) 0.04 0.3 0.34Z Z j j j pu0 0Line Generator= + = + = Z1 ( ) ( ) 0.1 0.1 .2Z Z j j j0 pu1 1Line Generator= + = + = Z2 ( ) ( ) 0.1 0.1 .2Z Z j j j0 pu2 2Line Generator= + = + = Zn .05j0 pu=for L-G fault

Ia1 Z Z Z ZE

3 n

a

0 1 2= + + +

. . . ..

j j j j0 2 0 2 0 34 0 150 1= + + +

1.12j pu=−

IB 3 generator kV

generator MVA= .

1753 6 6 10

20 10 0 Amp3

6

# #

#= =

Fault current If ( )I I3 a B= 3( 1.12)(1750) 5897.6j j Amp= − =−Neutral Voltage Vn I Zf n=



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and Zn Z ZB pu#=

( . )

. .206 6

0 05 0 10892

# Ω= =

Vn 5897.6 0.1089#= Vn .642 2= VHence (D) is correct option.

MCQ 1.57 Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are

. , . ,IC P IC P IC20 0 3 30 0 4 301 1 2 2 3= + = + =Where P1 is the power in MW generated by unit i for ,i 1 2= and 3. Assume that all the three units are operating all the time. Minimum and maximum loads on each unit are 50 MW and 300 MW respectively. If the plant is operating on economic load dispatch to supply the total power demand of 700 MW, the power generated by each unit is(A) 242.86 ; 157.14 ; 300P P PMW MW and MW1 2 3= = =

(B) 157.14 ; 242.86 ; 300P P PMW MW and MW1 2 3= = =

(C) 300 ; 300 ; 100P P PMW MW and MW1 2 3= = =

(D) 233.3 ; 233.3 ; 233.4P P PMW MW and MW1 2 3= = =

SOL 1.57 The Correct option is (A).We know that Optimal Generation IC1 IC2= , and P 3003 = MW (maximum load) IC3 30= (Independent of load) . P20 0 3 1+ . P30 0 4 2= + . .P P0 3 0 41 2− 10= ...(1) P P P1 2 3+ + 700= P P 3001 2+ + 700= P P1 2+ 400= ...(2)From equation (1) and (2) P1 242.8= MW P2 .157 14= MW

MCQ 1.58 A list of relays and the power system components protected by the relays are given in List-I and List-II respectively. Choose the correct match from the four choices given below:

Group I Group II

P Distance relay 1. Transformers

Q Under frequency relay 2. Turbines

R Differential relay 3. Busbars

S Buchholz relay 4. Shunt capacitors



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5. Alternators

6. Transmission linesCodes: P Q R S(A) 6 5 3 1(B) 4 3 2 1(C) 5 2 1 6(D) 6 4 5 3

SOL 1.58 The Correct option is (A).For transmission line protection-distance relayFor alternator protection-under frequency relayFor bus bar protection-differential relayFor transformer protection-Buchholz relay

MCQ 1.59 A generator delivers power of 1.0 p.u. to an infinite bus through a purely reactive network. The maximum power that could be delivered by the generator is 2.0 p.u. A three-phase fault occurs at the terminals of the generator which reduces the generator output to zero. The fault is cleared after tc second. The original network is then restored. The maximum swing of the rotor angle is found to be 110maxδ = electrical degree. Then the rotor angle in electrical degrees at t tc= is(A) 55 (B) 70

(C) 69.14 (D) 72.4

SOL 1.59 The Correct option is (C).

We know by equal area criteria

( )PS m 0δ δ− sinP dmaxC

m δ δ=δ

δ#

( )sinPmax m0 0δ δ δ− [ ]cos cosPmax m0δ δ= − ...(1) Pmax 2= P0 sinP 1max 0δ= = 0δ 30c= maxδ 110c= (given)Now from equation (1)

( )sin2 30 110 30 180c π− [ ]cos cos2 110c cδ= −



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.50 18080

#π .342cos 0cδ= +

cos cδ .698 .3420 0= − cδ .69 138c=

MCQ 1.60 A three-phase alternator generating unbalanced voltages is connected to an unbalanced load through a 3-phase transmission line as shown in figure. The neutral of the alternator and the star point of the load are solidly grounded. The phase voltages of the alternator are 10 0 , 10 90 , 10 120E E EV V Va b cc c c+ + += = − = . The positive-sequence component of the load current is

(A) 1.310 107c+ − A (B) 0.332 120c+ − A

(C) 0.996 120c+ − A (D) 3.510 81c+ − A

SOL 1.60 The Correct option is (D).a Both sides are granted

So, Ia 5 90ZE

j210 0

a

a c c+ += = = −

Ib .ZE

j310 90 3 33 180

b

b c c+ += = − = −

Ic .ZE

j410 120 2 5 30

c

c c c+ += = =

We know Ia1 [ ]I I I31

a b c2α α= + +

where 1 120 1 2402&c c+ +α α= =

Ia1 [5 90 3.33 180 120 2.5 240 30 ]31 c c c c c+ + += − + − + + +^ ^h h

Ia1 [ . . ]31 5 90 3 33 60 2 5 270c c c+ + += − + − +

[ . . . ]j j j31 5 1 665 2 883 2 5= − + − −

[ . . ]j31 1 665 10 383= −

. .3 5 80 89c+= −

MCQ 1.61 For the n-channel enhancement MOSFET shown in figure, the threshold voltage



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2Vth = V. The drain current ID of the MOSFET is 4 mA when the drain resistance RD is 1 kΩ.If the value of RD is increased to 4 kΩ, drain current ID will become

(A) 2.8 mA (B) 2.0 mA

(C) 1.4 mA (D) 1.0 mA

SOL 1.61 For a n -channel enhancement mode MOSFET transition point is given by, V ( )DS sat V VGS TH= − 2V voltTHa = V ( )DS sat V 2GS= −From the circuit, VDS VGS=So V ( )DS sat 2V V V 2( )DS DS DS sat&= − = + VDS V> ( )DS sat

Therefore transistor is in saturation region and current equation is given by. ID ( )K V VGS TH

2= − 4 ( 2)K VGS

2= −VGS is given by V VGS DS= I R10 D D= − 10 4 1#= − 6 Volt=So, 4 (6 2)K 2= −

K 41=

Now RD is increased to 4 kΩ, Let current is I 'D and voltages are V V' '

DS GS=Applying current equation. I '

D ( )K V V'GS TH

2= −

I 'D ( 2)V

41 '

GS2= −

V V' 'GS DS= 10 I R' '

D D#= − 10 4I '

D= −So, 4I '

D (10 4 2)I 'D

2= − − 4I '

D (8 4 )I 'D

2= − 4I '

D 16(2 )I 'D

2= − I '

D 4(4 ' 4 )I I 'D D2= + −

4 'I 17 16D2 − + 0=



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'I D2 2.84 mA=


MCQ 1.62 Assuming the operational amplifier to be ideal, the gain /v vout in for the circuit shown in figure is

(A) 1− (B) 20−

(C) 100− (D) 120−

SOL 1.62 Let the voltages at input terminals of op-amp are v- and v+ respectively.So, 0v v= =+ - (ideal op-amp)

Applying node equation at negative terminal of op-amp,

v v1

010

0in x− + − 0= ...(1)

At node x

v v v v10

010 1

0x x out x− + − + − 0=

10v v v vx x out x+ − + 0= 12 vx vout=

vx v12out=

From equation (1),

v v1 10in x+ 0=

vin v120

out=−

vv

in

out 120=−




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MCQ 1.63 A voltage signal sin t10 ω is applied to the circuit with ideal diodes, as shown in figure, The maximum, and minimum values of the output waveform Vout of the circuit are respectively

(A) 10 V+ and 10 V− (B) 4 V+ and 4 V−

(C) 7 V+ and 4 V− (D) 4 V+ and 7 V−

SOL 1.63 In the positive half cycle (when 4V V>in ) diode D2 conducts and D1 will be off so the equivalent circuit is,

Vout 4 Volt= +

In the negative half cycle diode D1 conducts and D2 will be off so the circuit is,

Applying KVL 10I IV 4 10in − + − 0=

V20

4in + I=

10V Vin =− (Maximum value in negative half cycle)

So, I 20

10 4103 mA= − + =−



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V V10

in out− I=

V10

10 out− − 103=−

Vout ( )10 3=− − Vout 7=− voltHence (D) is correct option.

MCQ 1.64 The circuit of figure shows a 555 Timer IC connected as an astable multi-vibrator. The value of the capacitor C is 10 nF. The values of the resistors RA and RB for a frequency of 10 kHz and a duty cycle of 0.75 for the output voltage waveform are

(A) 3.62 , 3.62R Rk kA BΩ Ω= =

(B) 3.62 , 7.25R Rk kA BΩ Ω= =

(C) 7.25 , 3.62R Rk kA BΩ Ω= =

(D) 7.25 , 7.25R Rk kA BΩ Ω= =

SOL 1.64 In the circuit, the capacitor charges through resistor ( )R RA B+ and discharges through RB . Charging and discharging time is given as.

TC 0.693( )R R CA B= + TD 0.693 R CB=

Frequency . ( )

fT T T R R C1 1

0 693 21

D C A B= =

+=

+

. ( )R R0 693 2 10 10

1A B

9# #+ - 10 103#=

.14 4 103# R R2A B= + ...(1)

Duty cycle TTC= .0 75=

. ( ). ( )

R R CR R C

0 693 20 693

A B

A B

++

43=

R R4 4A B+ R R3 6A B= +



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RA R2 B= ...(2)From (1) and (2) R2 A .14 4 103#= RA 7.21 kΩ=and RB 3.60 kΩ=Hence (C) is correct option.

MCQ 1.65 The simplified block diagram of a 10-bit A/D converter of dual slope integrator type is shown in figure. The 10-bit counter at the output is clocked by a 1 MHz clock. Assuming negligible timing overhead for the control logic, the maximum frequency of the analog signal that can be converted using this A/D converter is approximately

(A) 2 kHz (B) 1 kHz

(C) 500 Hz (D) 250 Hz

SOL 1.65 Maximum frquency of input in dual slop A/D converter is given as Tm T2n

C=

where fm T1 maximum frquency of inputm"=

fC T1 clock frequencyC"=

so fm f2nC= , n 10=

1102410 kHz

6

= = (approax)


MCQ 1.66 The boolean expression X Y Z XYZ XYZ XYZ XYZ+ + + + can be simplified to(A) XZ XZ YZ+ + (B) XY YZ YZ+ +

(C) XY YZ XZ+ + (D) XY YZ XZ+ +

SOL 1.66 The Correct option is (B).Given boolean expression can be written as, F XYZ X YZ XYZ XYZ XYZ= + + + + ( ) ( )X YZ YZ X X XY Z Z= + + + + XYZ YZ XY= + + ( ) ( )( )YZ Y X X Z A BC A B A Ca= + + + = + +



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( )( )YZ Y X X X Z= + + + ( )YZ Y X Z= + + YZ YX YZ= + +

MCQ 1.67 The shift register shown in figure is initially loaded with the bit pattern 1010. Subsequently the shift register is clocked, and with each clock pulse the pattern gets shifted by one bit position to the right. With each shift, the bit at the serial input is pushed to the left most position (msb). After how many clock pulses will the content of the shift register become 1010 again ?

(A) 3 (B) 7

(C) 11 (D) 15

SOL 1.67 The Correct option is (B).

X = X X1 05 , Y X2=Serial Input [ ]Z X Y X X X1 0 25 5 5= =Truth table for the circuit can be obtain as.

Clock pulse Serial Input Shif register

Initially 1 1010

1 0 1101

2 0 0110

3 0 0011

4 1 0001

5 0 1000

6 1 0100

7 1 1010So after 7 clock pulses contents of the shift register is 1010 again.

MCQ 1.68 An X-Y flip-flop, whose Characteristic Table is given below is to be implemented



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using a J-K flip flop

(A) ,J X K Y= = (B) ,J X K Y= =

(C) ,J Y K X= = (D) ,J Y K X= =

SOL 1.68 The Correct option is (D).Characteristic table of the X-Y flip flop is obtained as.

X Y Qn Qn+1

0 0 0 1

0 0 1 1

0 1 0 0

0 1 1 1

1 0 0 1

1 0 1 0

1 1 0 0

1 1 0 0

Solving from k-map

Characteristic equation of X-Y flip flop is Qn 1+ Y Q XQn n= +Characteristic equation of a J-K flip-flop is given by Qn 1+ KQ J Qn n= +by comparing above two characteristic equations J Y= , K X=

MCQ 1.69 A memory system has a total of 8 memory chips each with 12 address lines and 4 data lines, The total size of the memory system is



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(A) 16 kbytes (B) 32 kbytes

(C) 48 kbytes (D) 64 kbytes

SOL 1.69 The Correct option is (A).Total size of the memory system is given by. ( )2 4 812# #= bits 2 814 #= bits 214= Bytes 16 K= bytes

MCQ 1.70 The following program is written for an 8085 microprocessor to add two bytes located at memory addresses 1FFE and 1FFFLXI H, 1FFEMOV B, MINR LMOV A, MADD BINR LMOV M, AXOR AOn completion of the execution of the program, the result of addition is found(A) in the register A

(B) at the memory address 1000

(C) at the memory address 1F00

(D) at the memory address 2000

SOL 1.70 Executing all the instructions one by one. LXI H,1FFE ( (H 1F) , L FE)H H& = = MOV B,M B& Memory [HL] Memory [1FFE]= = INR L L& ( (L 1) FF)H H= + = MOV A,M A& Memory [HL] Memory [1FFF]= = ADD B A& A B= + INR L L& ( ( (L 1) FF) 1) 00H H H= + = + = MOV M,A Memory [HL]& A= Memory [1F00] A= XOR A A& A XOR A= 0=So the result of addition is stored at memory address 1F00.Hence (C) is correct option.

MCQ 1.71 A control system with certain excitation is governed by the following mathematical equation



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dtd x

dtdx x

21

181

2

2+ + 10 5 2e et t4 5= + +− −

The natural time constant of the response of the system are(A) 2 sec and 5 sec (B) 3 sec and 6 sec

(C) 4 sec and 5 sec (D) 1/3 sec and 1/6 sec

SOL 1.71 Given equation

dtd x

dtdx x2

1181

2

2

+ + e e10 5 2t t4 5= + +− −

Taking laplace on both sides we have

( ) ( ) ( )s X s sX s X s21

1812 + + s s s

104

55

2= + + + +

( ) ( )s s X s21

1812 + +

( )( )( )( ) ( ) ( )

s s ss s s s s s

4 510 4 5 5 5 2 4= + +

+ + + + + +

System response is,

( )X s ( )( )

( )( ) ( ) ( )

s s s s s

s s s s s s

4 5 21

181

10 4 5 5 5 2 42

=+ + + +

+ + + + + +

b l

( )( )

( )( ) ( ) ( )

s s s s s

s s s s s s

4 5 31

61

10 4 5 5 5 2 4=+ + + +

+ + + + + +

b bl l

We know that for a system having many poles, nearness of the poles towards imaginary axis in s -plane dominates the nature of time response. So here time constant given by two poles which are nearest to imaginary axis.

Poles nearest to imaginary axis

s1 31=− , s 6

12 =−

So, time constants sec

sec

3

61

2

ττ

==

)

Hence (B) is correct option

MCQ 1.72 The block diagram shown in figure gives a unity feedback closed loop control system. The steady state error in the response of the above system to unit step input is

(A) 25% (B) 0.75 %

(C) 6% (D) 33%

SOL 1.72 Steady state error for a system is given by



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ess ( ) ( )( )

limG s H ssR s

1s 0= +"

Where input ( )R s s1= (unit step)

( )G s s s153

115= + +b bl l

( )H s 1= (unity feedback)

So ess

( )( )

1

lim

s s

s s

115 1

45s 0=

+ + +"

b l

15 4515= + 60

15=

%ess 6015 100#= 25%=


MCQ 1.73 The roots of the closed loop characteristic equation of the system shown above (Q-5.55)

(A) 1− and 15− (B) 6 and 10

(C) 4− and 15− (D) 6− and 10−

SOL 1.73 Characteristic equation is given by ( ) ( )G s H s1 + 0=Here ( )H s 1= (unity feedback)

( )G s s s153

115= + +b bl l

So, 1 s s153

115+ + +b bl l 0=

( )( )s s15 1 45+ + + 0= 16 60s s2 + + 0= ( 6)( )s s 10+ + 0= s 6,=− 10−Hence (C) is correct option.

MCQ 1.74 The following equation defines a separately excited dc motor in the form of a differential equation

dtd

JB

dtd

LJK

LJK Va

2 2ω ω ω+ + =



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The above equation may be organized in the state-space form as follows

dtd

dtd P dt

dQVa

2

2ω

ω

ω

ω= +

R

T

SSSSS

>

V

X

WWWWW

H

Where the P matrix is given by

(A) 1 0JB

LJK2

− −= G (B)

0 1LJK

JB2

− −= G

(C) 0 1

LJK

JB2

− −= G (D) 1 0

JB

LJK2

− −= G

SOL 1.74 Given equation can be written as,

dtd

2

2ω J dtd

LJK

LJK Va

2β ω ω=− − +

Here state variables are defined as,

dtdω x1=

ω x2=So state equation is

x1o JB x LJ

K x LJK Va1

2

2=− − +

x2o dtdω= x1=

In matrix form

xx

1

2

o

o> H / / /B J K LJ x

xK LJ

V1 0 0 a

21

2=

− −+> > >H H H

dtd

dtd

2

2ω

ω

R

T

SSSS

V

X

WWWW

Pddt QVa

ω= +> H

So matrix P is

/ /B J K LJ

1 0

2− −> H


MCQ 1.75 The loop gain GH of a closed loop system is given by the following expression

( )( )s s sK2 4+ +

The value of K for which the system just becomes unstable is(A) K 6= (B) K 8=

(C) K 48= (D) K 96=



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SOL 1.75 Characteristic equation of the system is given by GH1 + 0=

( )( )s s s

K12 4

+ + + 0=

( )( )s s s K2 4+ + + 0= s s s K6 83 2+ + + 0=Applying routh’s criteria for stability

s3 1 8

s 2 6 K

s 1 K6

48−

s 0 K

System becomes unstable if K 648 0− = 48K& =


MCQ 1.76 The asymptotic Bode plot of the transfer function /[1 ( / )]K s a+ is given in figure. The error in phase angle and dB gain at a frequency of 0.5aω = are respectively

(A) 4.9c, 0.97 dB (B) 5.7c, 3 dB

(C) 4.9c, 3 dB (D) 5.7c, 0.97 dB

SOL 1.76 The maximum error between the exact and asymptotic plot occurs at corner frequency.Here exact gain(dB) at 0.5aω = is given by

( )gain dB. a0 5ω =

log logKa

20 20 1 2

2ω= − +

( . )

log logKaa

20 20 10 5 /

2

2 1 2

= − +; E



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.logK20 0 96= −Gain(dB) calculated from asymptotic plot at . a0 5ω = is logK20=Error in gain (dB) 20 (20 0.96)log logK K dB= − − .0 96= dBSimilarly exact phase angle at 0.5aω = is.

( ).

ha0 5

θ ωω =

tan a1 ω=− −a k

.tan aa0 51=− −

b l

2 .566 c=−Phase angle calculated from asymptotic plot at ( 0.5 )aω = is 22.5c−Error in phase angle . ( . )22 5 26 56c=− − − .4 9c=Hence (A) is correct option.

MCQ 1.77 The block diagram of a control system is shown in figure. The transfer function ( ) ( )/ ( )G s Y s U s= of the system is

(A) s s18 112

13

1+ +` `j j

(B) s s27 16

19

1+ +` `j j

(C) s s27 112

19

1+ +` `j j

(D) s s27 19

13

1+ +` `j j

SOL 1.77 Given block diagram

Given block diagram can be reduced as



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Where G1

s

s

1 1

1

3=+ b

b

l

l s 3

1= +

G2

s

s

1 1 12

1

=+ b

b

l

l s 12

1= +

Further reducing the block diagram.

( )Y s ( )G GG G

1 2 92

1 2

1 2= +

( ) ( )

( )

s s

s s

1 2 31

121 9

2 31

121

=+ + +

+ +

b b

b b

l l

l l

( )( )s s3 12 18

2= + + +

s s15 54

22=+ +

( 9)( 6)s s

2= + +

s s27 1 9 1 6

1=+ +a ak k


MCQ 1.78 The items in Group-I represent the various types of measurements to be made with a reasonable accuracy using a suitable bridge. The items in Group-II represent the various bridges available for this purpose. Select the correct choice of the item in Group-II for the corresponding item in Group-I from the following List-I List-IIP. Resistance in the milli- 1. Wheatstone Bridge ohm rangeQ. Low values of Capacitance 2. Kelvin Double BridgeR. Comparison of resistance 3. Schering Bridge



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which are nearly equalS. Inductance of a coil with 4. Wien’s Bridge a large time-constant 5. Hay’s Bridge 6. Carey-Foster BridgeCodes :(A) P=2, Q=3, R=6, S=5 (B) P=2, Q=6, R=4, S=5

(C) P=2, Q=3, R=5, S=4 (D) P=1, Q=3, R=2, S=6

SOL 1.78 The Correct option is (A).Kelvin Double bridge is used for measuring low values of resistances. ( 2)P "

Low values of capacitances is precisely measured by schering bridge ( 3)Q "

Inductance of a coil with large time constant or high quality factor is measured by hay’s bridge ( 5)R "

MCQ 1.79 A rectifier type ac voltmeter 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 Ω 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 100 V (rms) applied to the input terminals is

(A) 63.56 Ω (B) 69.93 Ω

(C) 89.93 Ω (D) 141.3 kΩ

SOL 1.79 Full scale deflection is produced by a dc current of 1 mA ( )Idc fs 1= mAFor full wave reactifier

( )Idc fs I2 m

π= , Im "peak value of ac current

1 mA .I

3 142 m=

Im .1 57= mA

Full scale ac current

( )Irms fs . .2

1 57 1 11= = mA



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V ( )( )R R Is m rms fs= + 100 ( 100)(1.11 )R mAs= +

(1.11 )

100mA

R 100s= +

100 900# R 100s= + Rs .89 9= kΩHence (C) is correct option.

MCQ 1.80 A wattmeter reads 400 W when its current coil is connected in the R-phase and its pressure coil is connected between this phase and the neutral of a symmetrical 3-phase system supplying a balanced star connected 0.8 p.f. inductive load. This phase sequence is RYB. What will be the reading of this wattmeter if its pressure coil alone is reconnected between the B and Y phases, all other connections remaining as before ?(A) 400.0 (B) 519.6

(C) 300.0 (D) 692.8

SOL 1.80 The Correct option is (B).First the current coil is connected in R-phase and pressure coil is connected between this phase and the neutral as shown below

reading of wattmeter W1 cosI VP P 1θ= , . .cos 0 8 36 861 1& cθ θ= =

400 cosI V3

LL

1θ=

400 .I V3

0 8L L#= ...(1)

Now when pressure coil is connected between B and Y-phases, the circuit is



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phasor diagram

angle 2θ 23.14 30 .54 14c c c= + =now wattmeter reading W2 cosV IYB L 2θ=

from equation (1) V IL L .0 8400 3#=

so W2 . .cos0 8400 3 53 14# # c=

.519 5= W

MCQ 1.81 The inductance of a certain moving-iron ammeter is expressed as10 3 ( /4)L H2θ θ μ= + − , where θ is the deflection in radians from the zero position.

The control spring torque is 25 10 6#- Nm/radian. The deflection of the pointer in

radian when the meter carries a current of 5 A, is(A) 2.4 (B) 2.0



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(C) 1.2 (D) 1.0

SOL 1.81 In a moving-iron ammeter control torque is given as

cτ K I ddL

21 2θ θ= =

WhereK " control spring constant"θ deflection

Given that L 10 3 42

θ θ= + −

ddL

θ 3 2 H/radθ μ= −b l

So,

(25 10 )c6

#τ θ= − ( )21 5 3 2 102 6

#θ= − −

b l

2θ 3 2θ= −

25 3 &

θ θ= .56 1 2= = rad.


MCQ 1.82 A 500A/5A, 50 Hz transformer has a bar primary. The secondary burden is a pure resistance of 1 Ω and it draws a current of 5 A. If the magnetic core requires 250 AT for magnetization, the percentage ratio error is(A) 10.56 (B) .10 56−

(C) 11.80 (D) .11 80−

SOL 1.82 The Correct option is (B).

Magnetizing current Im 1250 250= = amp

Primary current Ip 500= amp Secondary current Is 5= amp

Turn ratio n II

5500 100

s

p= = =

Total primary current ( )IT [primary current(I )]p2= +

[magnetising current ( )]I 2m

IT I Ip m2 2= +

( ) ( )500 2502 2= + .559 01= amp

Turn ratio n' . .II

5559 01 111 80

s

T= = =

Percentage ratio error n3 100n

n n#= −

ll



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..

111 80100 111 80 100#= − . %10 55=−

MCQ 1.83 The voltage-flux adjustment of a certain 1-phase 220 V induction watt-hour meter is altered so that the phase angle between the applied voltage and the flux due to it is 85c(instead of 90c). The errors introduced in the reading of this meter when the current is 5 A at power factor of unity and 0.5 lagging are respectively(A) 3.8 mW, 77.4 mW (B) .3 8− mW, .77 4− mW

(C) .4 2− W, .85 1− W (D) 4.2 W, 85.1 W

SOL 1.83 The Correct option is (C).Power read by meter ( )sinP VIm 3 φ= −Where

"3 Phase angle between supply voltage and pressure coil flux."φ Phase angle of load

Here 3 85 , 60c cφ= = .cos 0 5a φ ="So measured power Pm ( )sin200 5 85 60# c c= − sin1100 25c= .464 88= W

Actual power PO cosVI φ= .220 5 0 5# #= 550= W Error in measurement P Pm O= − .464 88 550= − .85 12=− W For unity power factor cosφ 1= φ 0c=

So Pm ( )sin220 5 85 0# c c= − .1095 81= W PO cos220 5 0# c= 1100=Error in Measurement .1095 81 1100= − .4 19=− W

MCQ 1.84 Group-II represents the figures obtained on a CRO screen when the voltage signals sinV V tx xm ω= and ( )sinV V ty ym ω Φ= + are given to its X and Y plates respectively

and Φ is changed. Choose the correct value of Φ from Group-I to match with the corresponding figure of Group-II.



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Group-I

P. 0Φ =

Q. /2πΦ =

R. /3 2< <π πΦ

S. /3 2πΦ =

Group-II

Codes :(A) P=1, Q=3, R=6, S=5 (B) P=2, Q=6, R=4, S=5

(C) P=2, Q=3, R=5, S=4 (D) P=1, Q=5, R=6, S=4

SOL 1.84 We can obtain the Lissaju pattern (in X-Y mode) by following method.For 0cφ = , Vx sinV txm ω= Vy ( 0 )sin sinV t tym cω ω= + =Draw Vx and Vy as shown below



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Divide both Vy and Vx equal parts and match the corresponding points on the screen. Similarly for φ 90c= Vx sinV txm ω= Vy ( 90 )sinV tym cω= +

Similarly for 23φ π=



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we can also obtain for 0 23< <φ π


MCQ 1.85 In the circuit shown in Fig. Q.85, the current gain ( )β of the ideal transistor is 10. The operating point of the transistor ( , )V ICC C is

(A) (40 , 4 )V A (B) (40 , 5 )V A

(C) ( , 4 )V A0 (D) (15 ,4 )V A

SOL 1.85 The Correct option is ().

MCQ 1.86 A phase-controlled half-controlled single-phase converter is shown in figure. The control angle 30cα =

The output dc voltage wave shape will be as shown in



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SOL 1.86 The Correct option is ( ).

MCQ 1.87 A chopper is employed to charge a battery as shown in figure. The charging current is 5 A. The duty ratio is 0.2. The chopper output voltage is also shown in the figure. The peak to peak ripple current in the charging current is

(A) 0.48 A (B) 1.2 A

(C) 2.4 A (D) 1 A

SOL 1.87 The Correct option is (A).In the chopper during turn on of chopper V -t area across L is,

V dtLT

0

on# L dt

di dt LdiT

i

i

0 min

maxon= =b l# #

( )L i i L Imax min Δ= − = ^ h

V -t are applied to ‘L ’ is (60 12)Ton= − T48 on=



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So now volt area

IΔ LT48 on= . 0.48

20 1048 0 2 10

3

3

#

# #= =−

− A

MCQ 1.88 An inverter has a periodic output voltage with the output wave form as shown in figure

When the conduction angle 120cα = , the rms fundamental component of the output voltage is(A) 0.78 V (B) 1.10 V

(C) 0.90 V (D) 1.27 V

SOL 1.88 The Correct option is (A).

Output voltage V0 4 /sin sin sinnV nd n t n 2

, ,

S

n 1 3 5 π ω π=3

=b ^ ^ ^l h h h/

RMS value of fundamental component

Vrms(fundamental) sinV d2

4 1S#

π=

120cα = , 120 60d d2 &c c= =

Vrms(fundamental) sinV2

4 60S# c

π=

0.78 0.78V VS= =

MCQ 1.89 With reference to the output wave form given in above figure , the output of the converter will be free from 5th harmonic when(A) 72cα = (B) 36cα =

(C) 150cα = (D) 120cα =

SOL 1.89 The Correct option is (A).After removing 5th harmonic d5 , ,0 2π π=



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Pulse width , ,d2 0 52

54α π π= = =

, ,0 72 144c c c=

MCQ 1.90 An ac induction motor is used for a speed control application. It is driven from an inverter with a constant /V f control. The motor name-plate details are as follows (no. of poles = 2):415 :3 :50 :2850V V f NV V Hz rpmPh

The motor runs with the inverter output frequency set at 40 Hz, and with half the rated slip. The running speed of the motor is(A) 2400 rpm (B) 2280 rpm

(C) 2340 rpm (D) 2790 rpm

SOL 1.90 The Correct option is (C). NSa 3000 rpm= Na 2850 rpm=

SFL .30003000 2850 0 05= − =

where by ( / )V f control

Nsb 3000 5040= b l

2400 rpm= N2 new running speed of motor=

1 .2400 20 05= −b l

2340 rpm=



PUBLISHING FOR GATE

Answer Sheet

1. (C) 19. (C) 37. (D) 55. (B) 73. (C)2. (B) 20. (D) 38. (B) 56. (D) 74. (A)3. (A) 21. (C) 39. (D) 57. (A) 75. (C)4. (A) 22. (A) 40. (B) 58. (A) 76. (A)5. (*) 23. (A) 41. (*) 59. (C) 77. (B)6. (D) 24. (A) 42. (C) 60. (D) 78. (A)7. (C) 25. (B) 43. (D) 61. (A) 79. (C)8. (D) 26. (A) 44. (D) 62. (D) 80. (B)9. (A) 27. (D) 45. (A) 63. (D) 81. (C)10. (D) 28. (D) 46. (C) 64. (C) 82. (B)11. (C) 29. (B) 47. (A) 65. (B) 83. (C)12. (B) 30. (A) 48. (B) 66. (B) 84. (A)13. (B) 31. (C) 49. (D) 67. (B) 85. (*)14. (C) 32. (C) 50. (B) 68. (D) 86. (*)15. (B) 33. (D) 51. (B) 69. (A) 87. (A)16. (C) 34. (D) 52. (A) 70 (C) 88. (A)17. (B) 35. (B) 53. (D) 71 (B) 89. (A)18. (D) 36. (B) 54. (D) 72 (A) 90. (C)

gate ee 2003 with solutions

Engineering

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