Set 1 (One Mark Questions)
1. The equivalent resistance of four parallel resis- tances is 40 Ω. The currents through them are 0.4, 0.5, 0.3 and 0.2 A. The lowest value of resistance is –––.
2. In the given circuit if the current through the resis- tance R is zero, what is the value of I?
I 20V
5Ω
5Ω
5Ω
− +
R = 5Ω
(a) 4 A (b) 2 A (c) 4 5
A (d) 5 4
A
3. The network shown in Fig. (a) can be replaced by Fig. (b) when I
C and R
C, respectively, are –––.
10Ω
20V
20Ω
− +
(a)
20Ω RC
IC
(b)
4. Current through the voltage source in the following circuit is –––.
0.5A 10Ω
20V
PRACTICE EXERCISES 113
2Ω
2Ω
1V 2H
1Ω
+−
(a) 1 3
s (b) 1 4
s (c) 1 2
s (d) 1 s
15. In the circuit given below, the Norton equivalence current in amperes w.r.t. to the terminals P and Q is _____.
−20jΩ 40jΩ
20jΩ
P
Q 25Ω
20∠0°
16. In the circuit shown in the figure below, the value of voltage source E is _____.
2
1 V2
V1
0V
4V 6V
10V 7V 3V
E
− −
−
−
+
+ + +
(a) 14 V (b) 21 V (c) 7 V (d) 0 V 17. Find V
o in the circuit shown in figure below.
3Ω
12V
Vo
4Ω 6Ω
3Ω
− +
(a) 2 V (b) −3 V
(c) +3 V (d) None of the above (a) 20∠ °90 (b) 18∠89 26. °
(c) 17∠89 26. ° (d) 15 59. ∠89 26. °
9. In the figure given below, the input impedance is given by
Zin
j4
j10 j10 j10
j20
(a) 6 jΩ (b) 8 jΩ (c) 4 jΩ (d) 10 jΩ
10. In the circuit given in the figure below, determine R.
R
14Ω V
2Ω
100V 40V
50V
40V 100V
10A 5A
0V 10A
15A 1Ω
+− +
−
− +
−
+ −
− + +
11. In the circuit given below, determine V
ab. a
b 2Ω
2Ω
1V 3A
1Ω
−
+ −
− + +
− +
(a) 2.5 V (b) 3.5 V (c) 7 V (d) 5 V
13. Find the number of twigs for the given connected graph.
14. Determine the time constant of the circuit shown in the following figure.
23. Current supplied by the AC current source in the figure below is
R 14A 14A
L C
10A 3A
(a) 20 A (b) 15.6 A
(c) 14.6 A (d) None of the above 24. The circuit given below is initially in steady state.
Switch K is opened at t = 0, the time constant of the circuit is
15Ω 0.4V
10V 4H
20Ω K t = 0
VR
−
− + +
− +
(a) 0.55 s (b) 0.35 s (c) 0.40 s (d) 0.50 s 25. The value of current i(t) in the following circuit is
_____.
2Ω 4Ω
20V
2F 4H
t = 0 i(t)
26. In the circuit given below, the switch K is closed at t = 0. The time constant and initial value of cur- rent i(t) are –––.
20Ω
20V
4F 2F 4V 5V i(t) K
− +
− +
27. In a two-terminal network open circuit, voltage measured at the same terminals by an electronic voltmeter is 200 V. A short circuit current measured 18. Determine the time constant of the circuit shown
in the figure given below.
1Ω 1Ω
1V 1F
19. Find the time constant of the circuit shown in the figure given below.
2Ω 2Ω
2Ω
10V 1F 1F
2F
20. In the circuit given below, current I
2 = 3 A when the value of R
1 is 20 Ω. Find the value of I
2 with R1 = 10 Ω.
20Ω 4A
N1
R1
I1 I2
N2
(a) 5 A (b) 2 A (c) 4 A (d) 3 A
21. The circuit given below is initially in steady state.
The switch S is closed at t = 0. Find values of V and dV/dt at t = 0+.
3Ω S
5Ω 2F
V 2H
10A
22. In the figure given below, S is in position `a’ for a time t. At t = 0, S is moved to position `b’. At t = 0+, the current I in R = 2 W is given by
C
a b
3A R = 2Ω
1Ω
4V I
(a) 4 A (b) 0 A (c) 1 A (d) 2 A
PRACTICE EXERCISES 115
1000Ω
2000Ω
10µF
100V
a b
S
i
V
(a) 100 V, 110 mA (b) 110 V, 200 mA (c) 100 V, 100 mA (d) 100 V, 150 mA
33. A delta connected load is having impedance Z Z
b = 5 in each branch. So, the corresponding star connection having impedance Z
b in each branch is
Zb Zb
Zb
1 1
1
3 2
3 2
3
⇒
√5Z
√5Z
√5Z
(a) 5
3 Z
(b) 5
3 Z
(c) 5 3
Z (d) 5
3 Z
34. For the circuit given below, determine R
ab.
a b
4Ω 3Ω
1Ω 5Ω
2Ω
35. In the circuit given below when the voltage V is 20 V, the current i is 2 A. If the supply voltage across c−d is 200 V, the short circuiting current flowing through terminal a−b will be _____.
Linear passive N/W E i
a
b
c
d
36. In the circuit shown in the following figure, the voltage across the 2 Ω resistor is 20 V. The 5 Ω resistor between terminals A and B can be replaced by an
at the same terminals by an ammeter of negligi- ble resistance is 5 A. If load resistance of 100 Ω is connected at the same terminals, then the cur- rent in the load resistor will be _____.
28. If the transmission parameters of the network given below are A = C = 2, B = 4 and D = 5. The value of Z input is
Two-port N/W
Zin
V1 V2
20Ω
(a) 20
5
W (b)
44 45
W (c) 40
45
W (d) 40
44 W
29. The Y-parameter of the following network is 0 1 2
1 2 1
− / /
(a) non-reciprocal and active (b) non-reciprocal and passive (c) reciprocal and active (d) reciprocal and passive 30. Determine Y
12 for the network shown in the figure given below.
10Ω 5Ω
20Ω
YA YB
YC
31. Find h
12 of the network shown in the figure given below.
R R
V1 R I1
− +
V2
− + I2
32. Switch S in moved from `b’ to `a’ of the circuit given below. What are the values of V(0+) and i(0+)?
50V
5Ω 3Ω
10Ω 20Ω
V
(a) 1.5 A (b) 1.40 A
(c) 1.42 A (d) None of above
41. Equivalent resistance between A and B terminals is
A B
1Ω 1Ω
1Ω 1Ω
1Ω
(a) 5 6
W (b) 6 5
W (c) 4 3
W (d) 8 3
W 42. The total power absorbed in the given circuit is
3V 3V
1A
0.25A 0.25A
0.75A 4Ω
− +
(a) 3 W (b) 4 W (c) 5 W (d) 6 W 43. In the following circuit, current through the induc-
tor is —————————.
L
V R C
4A 5A
5A
3A
− +
44. Determine the angle between the V
S and V
L.
VS VL 17.32Ω j10Ω
− +
− + 5Ω
2Ω 10A
5A 5A 20V
A
B 1Ω
5Ω 3Ω
R1 R1
E
−
−
+ +
(a) ideal voltage source of 25 V with the positive terminal upwards.
(b) ideal voltage source of 25 V with negative ter- minal upwards.
(c) current source of 2 A upwards.
(d) current source of 2 A downwards.
37. Find the value of power delivered by dependent current source from the circuit below.
10Ω
10Ω A
I
− +
Vx Vx=20V 4
1
(a) 300 W (b) 400 W
(c) 350 W (d) 250 W
38. R, L, C are connected in parallel across a sinusoi- dal voltage source of 250 V. If the current through inductor, capacitor and resistance are 3 A, 4 A and 3 A, respectively, find the value of X
L.
R
250V L C
10A
4A
3A 3A
(a) 100 Ω (b) 80 Ω
(c) 83.3 Ω (d) none of above
39. Find value of R so that the current through R
L
is zero.
R
50V RL = 10Ω
4Ω
(a) 0 Ω (b) 5 Ω (c) 10 Ω (d) 15 Ω 40. Find the value of current through 5 Ω resistance.
PRACTICE EXERCISES 117
(a) 214 VAR (b) 0 VAR (c) 314 VAR (d) 210 VAR
55. How many 100 W/110 V incandescent lamps con- nected in series consume total power as a single 50 W/110 V incandescent lamp?
56. Power supplied by the following voltage source is
Ix−4 Ix−6
Ix 2A
4A 2Ω
2Ω
2Ω
5Ω 2Ω
10V +−
(a) —12 V (b) 10 V (c) 0 V (d) 4 V 57. A voltage source of 240 V having an internal
impedance of (4 − 5j ) is supplying power to a com- plex load impedance Z. What will be the maximum power transferred to the load?
58. In the following circuit, the value of R for maximum power to be delivered is _____.
RL
20Ω 2H
V = Vmcos 20t
59. Which one of the following theorems is convenient to determine the power dissipation in 10 Ω resistor?
10sin(100t) sin(200t) 0.02µF
5Ω 5mH 10Ω
− +
− +
(a) Thevenin’s (b) Maximum power transfer (c) Millman’s (d) Superposition
60. The dual of series RL circuit is a
(a) series RC circuit (b) parallel RC circuit (c) series RL circuit (d) parallel RL circuit (a) V
V
S
= L
2
∠ °90 (b) V V
L
= S
2
∠ °60 (c) V V
L = S∠ °60 (d) V V
L
= S∠ ° 2
90
45. Determine average and rms values of i t( )=5+3 2cos(100t+20)+5 2cos(200+10°). 46. The rms value of a half and full rectified sine wave
of 2 A is (a) I I
m m
2 2
, (b) I I
m m
2 2 , (c)
I I
m m
3 3
, (d) Cannot be determined
47. Find the average power being delivered to an imped- ance Z
L = 8 − 11j Ω by a current I= 5∠ °20A. 48. Find the average power delivered to a 4 Ω resistor
by the current
i1 = 2cos10t − 3cos20t A
49. Find the average power delivered to 4 Ω resistor by the current i
2 = 2cos10t − 3cos10t.
50. A parallel RLC circuit has w0 = 108 and Q = 20.
Given C = 20 pF, find R.
(a) 1 2
104
× W (b) 104Ω
(c) 2 × 104 Ω (d) 25 Ω
51. The Q-factor of series RLC circuit is 100. If all the components double, then the Q is
(a) 0.5Q (b) 4Q
(c) 2Q (d) does not change
52. The power delivered by the 20 V source shown in the following figure is—————————.
20V
i 4A
2A
20V 5Ω
− + +−
53. Power output for DC component of a full wave rectifier with maximum value of 10 A AC current and R
L = 10 Ω is given by
(a) 405.68 W (b) 134.22 W (c) 117.38 W (d) 120.40 W 54. In a series RLC circuit R = 30 Ω, X
L = 40 Ω, XC = 40 Ω connected across 220 V, 50 Hz supply.
Find the reactive power of the circuit.
Set 2 (Two Marks Questions)
1. In the circuit given below, voltage across 20 Ω resis- tor is 100 V. What is the total voltage across the combined circuit?
VS
100V 5Ω
10Ω
10Ω 5Ω
20Ω
2. In the circuit given below, the value of current in the 30 Ω resistance is
100V
A Z
Y
X 2Ω 30Ω 10Ω
20Ω 20Ω
20Ω
(a) 2 A (b) 2.3 A (c) 1.1 A (d) 3.1 A 3. In the circuit given below, the values of I
y and V
z are
10A
50V
20V 15Ω Iy
Vz 20Ω
5Ω 10Ω
5Ω
(a) 50 V, 2 A (b) 44.2 V, 2.5 A (c) 60 V, 2.5 A (d) 47.2 V, 2.5 A
4. For the circuit shown in the figure given below, determine
di dt
L(0+) and
dV dt
C(0+) .
VC iL
1mH 1µF u(−t)
100Ω
− + 61. Determine the current (I) and average power
(Pavg) in the circuit shown in the following figure.
I 20Ω 200V
200V
−
− +
− + + 100V∠0°
62. For the series RLC circuit, the phasor diagram at a certain frequency is shown in the figure given below. Then the operating frequency is
L R
VR VL
VC C
−
− +
− +
− + + V
VC V VR = IR
(a) f = 0 (b) f = f
0 (c) f < f
0 (d) f > f
0
63. In the circuit shown in the figure given below, steady state is reached with S open. S is closed at t = 0. Determine the current I in the 1 Ω resistor at t = 0+.
4V
S
L 1Ω
1Ω 1Ω
(a) 2 A (b)1 A
(c) 0 A (d) None of the above 64. In the circuit given below, find the value of V
that would result in a steady state current of 2 A through the inductor.
20Ω
20Ω 20Ω
V 2H
PRACTICE EXERCISES 119
9. In the given figure, R=1 5
W, L=1 6
H, C = 4 F has input voltage V(t) = 4sin3t. The resulting peak value of current I
m is i(t)
V(t) R L C
(a) 50 A (b) 44.72 A
(c) 54.7 A (d) 50.72 A
10. Determine the time constant in the following circuit.
10Ω
20Ω 2Ω
2H 2H
5A
1H
11. In the figure below, find voltage V(t).
I e3t
e4t 3Ω
4Ω 4H
V(t)
3Ω
− +
2 1
(a) 4e4t− 3e3t (b) 4(e4t− 3e3t) (c) 4(e4t− 3e3t) (d) None of the above 12. Resistance R
x = 10 Ω is connected between A−B terminals of the circuit given below. The current through A−B is _____.
2Ω 2Ω
A
B
10Ω 2Ω
5Ω 5A
5V +−
13. In the circuit given below, current I
x is given by
Ix 2Ω
4Ω 3Ω
4Ω 4V
10V
+− +−
5. Determine the potential difference between P and Q in the following circuit.
2Ω
10V
VP VQ
0V 10V 2A
4Ω +−
−
+ + −
8Ω 6Ω
−
+ + −
6. For the circuit shown in the following figure, V
S = 0, when I = 4 A. The value I for V
S = 16 V is
I
VS
IS 2Ω
2Ω 2Ω
+−
(a) 16 A (b) 8 A
(c) 4 A (d) 0 A
7. The circuit shown in the following figure acts as a load resistor of
I
V 4Ω
2Ω
2I V
+− −
+
(a) 4 3
W (b)
8 3
W
(c) 6 Ω (d) 2 Ω
8. Twelve 4 Ω resistances are used as edges to form a cube. Resistance between two diagonally opposite corners of cube is
4Ω 4Ω
4Ω 4Ω
4Ω 4Ω
4Ω
4Ω 4Ω
4Ω 4Ω
4Ω (a)
20 6
W (b)
40 6
W
(c) 20
3
W (d)
40 3
W
10V V
V1
C 1
2Ω 5Ω +
−
(a)1 F (b) 0.075 F
(c) 3.5 F (d) 0.150 F
19. Steady state is reached with S open. S is closed at t = 0. At t = 0+, the voltage across the capacitor VC and current i
C are given by
2A
S
1F H
1
2 Ω 1
2
(a) 1 V, 0 A (b) 0 V, 1 A (c) 0 V, 0 A (d) 1 V, 1 A
20. Steady state is reached with S open. S is closed at t = 0. Current I in R = 2 at t = 0+ is given by _____.
3A 1Ω R = 2Ω
S
1F I
21. For the circuit shown in the figure given below, the steady state current is _____.
5V 10sint
1Ω
1F 2H
i(t)
22. Determine the voltage across the inductor at t = 0+ and the total energy stored in steady state.
S 3Ω
2Ω
4H 4F
10V
t = 0
(a) 0 V, 100
3
J (b) 4 V,
200 9
J (c) 4 V,
100 3
J (d) 0 V,
200 9
J (a) 0.153 A (b) —0.153 A
(c) 0.316 A (d) Cannot be determind 14. For the circuit shown in the following figure deter-
mine the current i
L(t) for t ≥ 0 and time constant.
Assume i
L(0) = 10 A.
10Ω
20Ω 0.5H A
iL 4
iL
15. For the circuit shown in the figure given below, switch S is open for a long time and it is closed at t = 0. Determine current through the battery at t = 0+ and at t→ ∞.
1Ω
10V 1H 1F
t = 0 S
(a) 0 A and 10 A (b) 0 A and 0A (c) 10 A and 0 A (d) 10 A and 10 A
16. Find i(t) in the circuit in the figure given below for t > 0. Assume that the switch has been closed for a long time.
10V H
3Ω i
2Ω +−
t = 0
1 3
(a) 2 + 3e−15t (b) 3 + 2e−15t (c) 2 + 3e−5t (d) 3 + 2e−5t
17. Find V(t) for t > 0 in the circuit shown in the figure given below. Assume the switch has been open for a long time and is closed at t = 0. Calculate V(t) at t = 0.5.
6Ω 2Ω
10V V 50V
t = 0
+− +
− − +
F 1 3
18. In the given network, V = 5 V, dV dt/ = −20 V/s at time t, what is the value of C?
PRACTICE EXERCISES 121
27. S is open for a long time and steady is reached. S is closed at t = 0. Let i
L be the current in the induc- tor. At t = 0+, di
L/dt is –––.
1A
S
2Ω 2H
F 1 2
28. In the figure given below RC = 6 ms. The input voltage V( )t = 5sin203t. The output voltage Vo(t) is equal to
R
Vi C Vo(t)
(a) 5sin(203t+45°) (b) 2sin(20−3t+45°) (c)
5 2
203 45
sin( t+ °) (d) None of the above 29. In the circuit given below, find V
o(0+) as Vi(t) = 20 u(t).
2kΩ
Vi(0+) Vo(t)
6kΩ
+ +
− −
2µF 6µF
(a) 10 e−t/0.04 (b) 10 u(t) (c) 20 (d) 20e−t/0.005 30. Find the voltage output V
x from the circuit given in the following figure after 5 seconds.
(a) 10 V (b) 5 V
(c) 0 V (d) none of the above
Vi Vx
0.5µF
2kΩ 10V
5 s t
+
− 23. In the AC circuit given below, the value of phasor
voltage V
AB is
B
I2 I1
6Ω
6Ω
ZA ZB
−j4Ω j4Ω
A
10∠60°
(a) 40∠ °60 (b) 43 3. ∠ °60 (c) 43 3. ∠ °90 (d) 43 3. ∠ °30
24. For the circuit shown in the figure given below, the switch is closed for a long time and it is opened at t = 0. Determine v
C(t) and i
C(t) for t > 0.
iS S
5kΩ 20kΩ
10V 104iS VC
t = 0
2µF +
− i
+− −
+
(a) 20
3
25
e− t, −10− − 3
6 25
e t (b) 20
3
25
e− t, −10− − 3
3 25
e t (c)
20 6
25
e− t, −10 6
3 25
− −
e t
(d) 20
6
25
e− t, −10− − 3
3 25
e t 25. Find V
C(0), V
C(2 ms) and i(0+) for the circuit, when the switch is in position 1 for long time and it is moved to position 2 at t = 0.
800Ω
1 2 V
732Ω
50V 2µF
+
−
26. S is closed for a long time and steady state is reached. S is opened at t = 0. The voltage marked V is V
0 at t = 0+ and V
f at t= ∞. The values of V0 and V
f are, respectively, ––– and –––.
S V
2A
F 4Ω
4Ω
+
− 1
4
(a) 1 A (b) 0.5 A (c) 0.58 A (d) 0.7 A 35. The value of impedances Z
11 and Z
12 in following figure is
2Ω 3Ω 4Ω
4Ω 2Ω
2
2¢ 1
1¢
36. In a two-port reciprocal network, the output open circuit voltage by the input current is equal to (a) h
12 (b) Z
12
(c) Y
11 (d) B
37. In the given network, determine Z
in.
V1 V2
I1 I2
10Ω A = C = 1
B = 2 D = 3
+
− +−
38. If R
1 = R
2 = R
4 = 2R and R
3 = 4R. In the circuit given below, the reading of an ideal voltmeter is
R1 R4
R2 R3
B
10V A
+
− + V −
(a) 2.7 V (b) 3.7 V
(c) 1.7 V (d) 4.7 V
39. An ideal ammeter is connected between the terminal a and b. The reading of the ammeter is –––.
6Ω 6Ω
9.6V
a
b
6Ω 3Ω
40. In the circuit shown below, the voltage across 5 Ω resistor is 30 V. The 10 Ω resistor connected between terminals a and b can be replaced by an.
5Ω
4Ω
3Ω 5Ω
6Ω 10Ω R1
a b R2
V− + 31. When switch is opened at t = 0, the values of
V(0+) and dV
dt
(0+), are respectively.
200Ω 1
2 H V
S 2A
(a) 400 V, +160000 V/s (b) 500 V, 160000 V/s (c) 500 V, −160000 V/s (d) 400 V, −160000 V/s
32. In the circuit given below, the initial current is I(s) where s is a Laplace variable. The value of current I(s) is
5mH
5mV I(s) t = 0.0055 s
+
−
33. In the circuit given below switch was in position
`a’ for a long time, and is moved to position `b’ at time t = 0. The current i(t) to t > 0 is given by
20kΩ
i(t)
a b
10kΩ
0.1µF 0.5µF
0.4µF 100V
+
−
(a) 10 e−500t mA (b) 10 e−400t mA (c) 20 e−400t mA (d) 20 e−1000t mA 34. In the given circuit below, the current I
Z is equal to
6Ω
8Ω I
I1
I2
I3
+ 10jΩ
6jΩ
−j10Ω
20∠0°V
− +
PRACTICE EXERCISES 123
46. A series RLC circuit consists of L = 0.5 H, C = 50 mF and R = 40 Ω. Calculate voltage across capac- itor with 220 V AC rms and 50 Hz frequency.
(a) 140 V (b) 139.6 V
(c) 138.02 V (d) 142 V
47. Find the power dissipated across 10 Ω in the circuit below.
5A V
8Ω 4Ω
10Ω 10A
(a) 397.4 W (b) 300 W
(c) 297.5 W (d) None of the above 48. Find V
x in the given network.
5Ω
5Ω 20V
2Vx Vx +
+
−
−
49. Find the value of dependent current source as given the following figure.
4Ω 3Vx
3Ω 4A
10V i1 Vx
− + V1
(a) 4 V (b) 3.6 V
(c) 5.6 V (d) 4.5 V
50. Find the value of R in the figure given below
10Ω 6Ω
100V
10A R
(a) 1.5 Ω (b) 3.2 Ω
(c) 2.5 Ω (d) 4 Ω
(a) ideal voltage source 22.5 V with positive termi- nal upward.
(b) ideal voltage source 22.5 with positive terminal downward.
(c) current source of 22.5 A upward.
(d) None of the above.
41. Determine the power delivered by the 16 V source.
2 Ω 2Ω
2Ω
8A 16V
V
+ +
−
−
42. In the circuit shown in the figure given below, the dependent source is
1Ω 2Ω
V1
3Ω
5V 2A
− −
+ +
(a) absorbing 38.4 W (b) delivery 38.4 W (c) delivery 19.2 W (d) absorbing 19.2 W 43. In an AC circuit shown in the figure given below,
what value of C will result a unity power factor at the source?
220V 50Hz
C
Y
ZL = 30∠40° 44. The power factor of series RLC circuit at f = f
L is (a) 0.5 lead (b) 0.707 lead
(c) 0.5 lag (d) 0.707 lag
45. The current i(t) as shown in following figure is flowing through a resistor of 10 Ω. The average power dissipated in the resistor is ––––.
i(t)
t (ms) 10A
0 2ms 4 6
−10A
40Ω
10Ω
a I2 I3
I1
c
f e
b
d 30Ω
60Ω
50Ω 51. Find E
0 in the circuit given below.
E0 5Ω
5Ω 5Ω 2Ω
5Ω
10A 5A
+
−
52. In the circuit given in the following figure, power delivered across 10 Ω is given by
(a) 100.46 W (b) 9.60 W
(c) 90.6 W (d) none of the above