Lithium and sodium ion capacitors with high energy and power densities based on carbons from

ECE - 2007

1. The RC circuit shown in the figure is

(A) a low-pass filter (B) a high-pass filter (C) a band-pass filter (D) a band-reject filter

2. An independent voltage source in series with an independence ZS =RS + jXS

delivers a maximum average power to a load impedance ZL when

(A) j (B)

(C) j (D) j 3. In the AC network shown in the figure,

the phasor voltage VAB (in Volts) is

(A) 0 (B) 5∠3

(C) 12.5∠3 (D) 17∠3

ECE - 2008

4. The Thevenin equivalent impedance ZTh

between the nodes P and Q in the following circuit is

(A) 1 (B) 1 + s+

(C) 2 + s + (D)

ECE - 2009

5. An AC source of RMS voltage 20V with internal impedance Zs (1 2j) Ω feeds a load of impedance ZL (7 4j) Ω in the figure below. The reactive power consumed by the load is

(A) 8VAR (B) 16 VAR

(C) 28 VAR (D) 32 VAR ECE - 2010

6. The current I in the circuit shown is

(A) –j1 A (B) j1 A

(C) 0 A (D) 20 A

~

^{2 ∠} _{1 rad s} ^{1 5}

2 m 2 ∠

(1 2j)Ω

(7 4j)Ω 1

1

1 1

1

1

5∠3

A

j3 5

j3

B

5 R C

R C

+

+

7. For the parallel RLC circuit, which one of the following statements is NOT correct?

(A) The bandwidth of the circuit decreases if R is increased

(B) The bandwidth of the circuit remains same if L is increased

(C) At resonance, input impedance is a real quantity

(D) At resonance, the magnitude of input impedance attains its minimum value

ECE/EE - 2013

8. A source v (t) cos 1 t has an internal impedance of (4 + j3) . If a purely resistive load connected to this source has to extract the maximum power out of the source , its value in  should be

(A) 3 (B) 4

(C) 5 (D) 7

ECE/EE/IN - 2013

9. In the circuit shown below, if the source voltage Vs= 10053.13⁰ V then the Thevenin’s equivalent voltage in volts as seen by the load resistance RL is

(A) 10090⁰ (B) 8000⁰

(C) 80090⁰ (D) 10060⁰

10. Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is

(A) q q

(B) (1 q⁄ ) (1 q )

(C) (q q ) ( ⁄ ) (D) (q q ) ( ⁄ )

ECE - 2014

11. A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is

(A) (18 j 1.5) k (B) (18 j 1.5) k (C) (2 j 1.5) k (D) (2 j 1.5) k

12. A periodic variable x is shown in the figure as a function of time. The root-mean-square (rms) value of x is ______.

13. The circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is ________.

14. In the magnetically coupled circuit shown in the figure, 56 % of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ______ .

15. The steady state output of the circuit shown in the figure is given by

~

^{4 5 (1 16⁄ )}

1

6 cos (4t 3 )

4 4

i(t)

t x

1

T 2 T 2

j6 5

j4

 3

RL= 10

1

j4

y(t) = A( )sin( t ( )). If the amplitude | ( )| 0.25, then the frequency is

( ) 1

√3 ( ) 2

√3

( ) 1 ( ) 2

EE - 2006

1. In the figure the current source is 1 ∠0 A, R = 1Ω, the impedances are Zc = j Ω, and ZL = 2jΩ. The Thevenin equivalent looking into the circuit across X-Y is

(A) √2∠0 V, (1 + 2j) Ω (B) 2 ∠45⁰ V, (1 – 2j) Ω (C) 2 ∠45⁰ V, (1 + j) Ω (D) √2∠45⁰ V, (1 + j) Ω

2. An energy meter connected to an immersion heater (resistive) operating on an AC 230 V, 50 Hz, AC single phase source reads 2.3 units (kWh) in 1 hour.

The heater is removed from the supply and now connected to a 400 V peak to peak square wave source of 150 Hz. The power in kW dissipated by the heater will be

(A) 3.478 (B) 1.739

(C) 1.540 (D) 0.870

3. The circuit shown in the figure is energized by a sinusoidal voltage source

V1 at a frequency which causes resonance with a current of I.

The phasor diagram which is applicable to this circuit is

EE - 2007

4. In the figure transformer T1 has two secondaries, all three windings having the same number of turns and with polarities as indicated. One secondary is shorted by a 1 Ω resistor , and the other by a 15m

(D)

I

(C)

I

(B)

I I

(A) I

~

x

y

y(t) sin t

capacitor. The switch SW is opened (t =0) when the capacitor is charged to 5 V with left plate as positive At (t =0⁺) the voltage VP and Current IR are

(A) 25 V, 0.0A

(B) Very large voltage, very large current

(C) 5.0 V, 0.5 A (D) 5.0 V, 0.5 A

5. In the figure given below all phasors are with reference to the potential at point

“O”. The locus of voltage phasor YX as R is varied from zero to infinity is shown by

6. The R-L-C series circuit shown is supplied from a variable frequency voltage source.

The admittance locus of the network at terminals AB for increasing frequency is

EE - 2008

7. The Thevenin's equivalent of a circuit operating at = 5rad/s, has

= 3.71∠ 15.9⁰ V and

ZO =2.38 – j 0.667Ω. At this frequency, the minimal realization of the Thevenin's impedance will have a

Re Im

(D)

Im

Re (C)

Re Im

(B)

Im

Re (A)

C A

L

R

B

~

Locus of VYX

0 2V VYX

Locus of VYX

VYX

0 2V (A)

0 2V Locus of VYX

VYX

0 VYX

Locus of VYX

(C) 2V

(B) (D)

X Y

R

~

~

∠

∠

O

C

SW T1

+

Vp 25V

R IR

C +

(A) resistor and a capacitor and an inductor

(B) resistor and a capacitor (C) resistor and an inductor (D) capacitor and an inductor

8. The resonant frequency for the given circuit will be

(A) 1 rad /s (B) 2 rad /s

(C) 3 rad /s (D) 4 rad /s EE - 2010

9. If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then

(A) A, B are resistances and C, D capacitances

(B) A, C are resistances and B, D capacitances

(C) A, B are capacitances and C, D resistances

(D) A, C are capacitances and B, D resistances

EE - 2011

10. The r.m.s value of the current i(t) in the circuit shown below is

(A) (B) √

(C) 1 (D) √2

Common Data Q. 11 and Q. 12

The input voltage given to a converter is v 1 √2 sin(1 t)

The input drawn by the converter is i (1 √2 sin (1 t

3) 5√2 sin(3 t

4) 2√2 sin(5 t 6) 11. The input power of the converter is

(A) 0.31 (B) 0.44

(C) 0.5 (D) 0.71

12. The active power drawn by the convert is (A) 181 W

(B) 500 W

(C) 707 W (D) 887 W EE - 2012

13. A two–phase load draws the following phase currents:

i (t) sin( t ), i (t) cos ( t ).

These currents are balanced if 1 is equal to

(A) (B)

(C) ( 2 ) (D) ( 2 ) 14. The average power delivered to an

impedance (4 j3)  by a current 5 cos (100t+100) A is

(A) 44.2 W (B) 50 W

(C) 62.5 W (D) 125 W

1

~

1 1 1

i(t)

(1. sin t)

A C

B D

(b) Electrical equivalent

h h

(a) oupled tank

0.1H

1 1

EE - 2014

15. A combination of 1 µF capacitor with an initial voltage ( ) 2 in series with a 100 resistor is connected to a 20 mA ideal dc current source by operating both switches at t = 0s as shown. Which of the following graphs shown in the options approximates the voltage across the current source over the next few seconds?

16. A non-ideal voltage source has an internal impedance of . If a purely resistive load is to be chosen that maximizes the power transferred to the load, its value must be

(A) 0

(B) real part of (C) magnitude of

(D) complex conjugate of

17. A series RLC circuit is observed at two frequencies. At = 1 krad/s, we note that source voltage 1 ∠ results in a current . 3∠31 A. At

= 2krad/s, the source voltage 1 ∠ results in a current

2∠ A. The closest values for R,L,C out of the following options are

(A) 5 25 m 1

(B) 5 1 m 25

(C) 5 5 m 5

(D) 5 5 m 5 IN - 2006

1. Consider the AC bridge shown below. If

RC = 1 and ΔC

C <0.01, then ratio ⁰

s

V

V ^is

approximately equal to

(A) √1 (B)

(C) (D)

IN - 2007

2. In the circuit shown in the following figure, the current through the 1Ω resistor is

~

R

R C

t

2 ( )

t

2 ( )

t

2 ( )

t 2

( )

t t

(A) (1 + 5 cos 2t) A (B) (5 + cos 2t) A

(C) (1 5 cos 2t) A (D) 6A

3. Consider the AC bridge shown in the figure below, with R, L and C having positive finite values

Then

(A) if (B) if (C) if

√

(D) cannot be made zero

4. Consider the coupled circuit shown below.

At angular frequency , this circuit can be represented by the equivalent

T – network shown below.

Indicate the correct set of expressions for the impedances of the T – network (A) j ( )

j ( ) j

(B) j j j (C) j ( )

j ( ) j (D) j ( )

j ( ) j ( ) IN - 2008

5. In the circuit below the average power consumed by the 1 resistor is

(A) 50 W (B) 1050 W

(C) 5000 W (D) 10100 W 6. For the circuit shown below the voltage

across the capacitor is

(A) (10 + j 0)V (B) (100+j0)V

(C) (0 + j100)V (D) (0 – j100)V 7. For the circuit shown below the

steady-state current I is

I

1000 F 1mH

1Ω

V(t)= 5√2 cos(1000t)V

(10+j0)V 1 Ω

j1 Ω

j1 Ω

~

1 √2 sin (1 t)

1Ω

1 √2 cos (3 t) 1 mH

ig b

ig a

sin t

C = 0.25F

I = (5cos2t)A V = 1V

L=1H 1Ω

(A) 0A

(B) 5√2 cos (1000t)A (C) 5√2 cos (1 t ) (D) 5√2A

IN - 2010

Statement for Linked Answer Questions: 8

& 9

A coil having an inductance (L) of 10mH and resistance R is connected in series with an ideal 100 F capacitor (C). When excited by a voltage source of value 10√2 cos (1000t)V, the series RLC circuit draws 20W of power.

8. The value of the coil resistance R is (A) 1

(B) 2

(C) 4 (D) 5

9. The Q factor of the coil at an angular frequency of 1000rad/s is

(A) 1 (B) 2

(C) 4 (D) 5 IN - 2011

Common Data for Question 10 & 11 Consider the circuit shown below:

10. The current i(t) through the capacitor is (A) sin (5t) A

(B) cos (5t) A

(C) sin (5t – 45) A (D) 1 A

11. The average total power delivered by the sources is

(A) 0 W (B) 0.5 W

(C) 2 W (D) 4 W

2

cos(5t)

2 sin

(5t )

.1

i(t)

Answer Keys and Explanations

ECE

1. [Ans. C]

( ) ( )

( || 1 ⁄ ) ( 1 ⁄ ( || 1 ⁄ )) ( )

( )

( 3 1) ut J , _{( )}^{( )} _{( )}

(J ) s , (J ) s , (J ) t 1 ⁄ , (J ) J

3J 1 3⁄ Filter is band-pass filter.

2. [Ans. D]

For maximum power transfer, J

3. [Ans. D]

current impedance

53 ((5 3J)||(5 3J)) 5 3 34

1 173 4. [Ans. A]

Replace 10V by short circuit and 1A by open circuit

( 1). (1 1 ⁄ ) 2 1 ⁄ 1

5. [Ans. B]

The RMS current in the load is given by ⃗ ∠ tan ( ) 2∠ tan ( )

2 , reactive power 4 4 16 Also note that the active power consumed by the load 4 7 28

6. [Ans. A]

(L = 20 mH, C = 50 ) Nodal analysis at node A

2

j 1 1 j

* 1 j1 5 1 + 2

j1 2 1 [ j

2 1 j

2 ] j1 j1

1 j1 7. [Ans. D]

This is standard concept of parallel resonant circuit

8. [Ans. C]

| | √4 3 5Ω 9. [Ans. C]

1

j4 3 j4

j4 1 ∠53 13 5∠53 13 j4 2 ∠ 4∠ 2 ∠

8 9

8 9 10. [Ans. C]

fter series connection

~

¹

j

1 j 2 ∠

1

( )

11. [Ans. B]

Total ower (s) 1

.8∠ cos .8 1

.8∠ cos .8 18 1.5j

12. [Ans. *] Range 0.39 to 0.42

√1

T∫ x dt Equation of line 1

T 2⁄ (t ) 2t

T

√1

T*∫ (2t

T) dt

+

√1 T*4t

3T +

√4 3

1 8 1

√6 .4 8

13. [Ans. *] Range 9.99 to 10.01

For critically damped 1 1 2

1 2

1√ 1

2 1

4 √4 1 2 4

c 4 c 4

4 1

1 1 m 14. [Ans. *] Range 2.49 to 2.52

oupling coefficient given is .56 e know,

√ √ iven 4 5

.56 √4 5 2.5 4 15. [Ans. B]

y(t) ( ) sin[ t ( )]

| ( )| .25 By nodal analysis

x 1∠ x

1 cj x 2 cj ⁄ x [1

cj cj

2 ] 1∠

x [2 3 cj

2 ] 1∠

x 2

2 3 cj y x

2

1 2 3 cj

| ( )| 1 4

1

√4 9

9 12

2

√3 c

y(t)

sin t

x

4 4

i(t)

t x

1

T 2 T 2

(T 2⁄ , 1)

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