This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Advanced Problems Involving Complex Circuit Diagram – 1”.
1. The current wave shape is in the form of a square terminating at t = 4sec. The voltage across the element increases linearly till t = 4 sec and then becomes constant. The element is ____________
a) Resistance
b) Inductance
c) Capacitance
d) Semi-conductor
View Answer
Explanation: We know that, when a current pulse is applied to a capacitor, the voltage will have a waveform which rises linearly and then becomes constant towards the end of pulse. Hence, the element is a capacitor.
2. An infinite ladder is constructed with 1 Ω and 2 Ω resistor shown below. The current I flowing through the circuit is ___________
a) 8.18 A
b) 0 A
c) 9 A
d) 10 A
View Answer
Explanation: Equivalent Resistance, REQ = R = 1 + (2 || R)
Or, REQ = 2
So, I = \(\frac{18}{2}\) A = 9 A.
3. In the circuit given below, the phase angle of the current I with respect to the voltage V1 is __________
a) 0°
b) +45°
c) -45°
d) -90°
View Answer
Explanation: Net voltage applied to the circuit is 200∠0° V
I1 = \(\frac{200∠0°}{10.0}\)
= 20∠0° = 20
I2 = \(\frac{200∠0°}{10∠90°}\)
= 20∠-90° = -j20
I = I1 + I2 = 20(1-j) = 20\(\sqrt{2}\)∠45°
Voltage V1 = 100(1+j)
= 100\(\sqrt{2}\)∠45°
∴ Required phase angle = -45° – 45° = -90°.
4. Consider a circuit having 3 identical Ammeters A1, A2, A3 parallel to one another. The 1st Ammeter is in series with a resistance, the 2nd Ammeter is in series with a capacitor and the circuit is excited by a voltage V. If A1 and A3 read 5 and 13 A respectively, reading of A2 will be?
a) 8 A
b) 13 A
c) 18 A
d) 12 A
View Answer
Explanation: We can infer from the circuit,
A2 = \(\sqrt{13^2 – 5^2}\)
Or, A2 = \(\sqrt{169 – 25}\)
Or, A2 = \(\sqrt{144}\)
Or, A2 = 12 A.
5. In the circuit given below, the value of V1 is __________
a) 32.2 V
b) -25.23 V
c) 29.25 V
d) -29.25 V
View Answer
Explanation: \(\frac{V_A}{30} + \frac{V_A-40}{12} + \frac{V_A-V_B}{8}\) = 0
Or, 29 VA – 15 VB = 400
Also, \(\frac{V_B-V_A}{8} + \frac{V_B-120}{8}\) + 6 = 0
Or, VA = 65.23 V, VB = 99.44 V
V1 = 40-65.23 = -25.23 V.
6. For the three coupled coils shown in figure, KVL equation is ____________
a) V = (L1 + L2 + L3) \(\frac{di}{dt}\)
b) V = (L1 – L2 – L3 – M13) \(\frac{di}{dt}\)
c) V = (L1 + L2 + L3 + 2M12 – 2M23 – 2M13) \(\frac{di}{dt}\)
d) V = (L1 + L2 + L3 – 2M12 + 2M23 + 2M13) \(\frac{di}{dt}\)
View Answer
Explanation: M12 is positive while M23 and M13 are negative because of dots shown in figure.
So, the KVL equation is given by,
V = (L1 + L2 + L3 + 2M12 – 2M23 – 2M13) \(\frac{di}{dt}\).
7. A circuit excited by voltage V has a resistance R which is in series with an inductor and capacitor, which are connected in parallel. The voltage across the resistor at the resonant frequency is ___________
a) 0
b) \(\frac{V}{2}\)
c) \(\frac{V}{3}\)
d) V
View Answer
Explanation: Dynamic resistance of the tank circuit, ZDY = \(\frac{L}{RLC}\)
But given that RL = 0
So, ZDY = \(\frac{L}{0XC}\) = ∞
Therefore current through circuit, I = \(\frac{V}{∞}\) = 0
∴ VD = 0.
8. In the circuit given below, the value of resistance R is _________
a) 10 Ω
b) 18 Ω
c) 24 Ω
d) 12 Ω
View Answer
Explanation: Using KVL in loop 1, we get, 100 – 14I – 30 = 0
Or, I = \(\frac{70}{14}\) = 5 A
Then, VP – VQ = 14I – (15-I).1
= 70 – 10 = 60 V
∴ R = \(\frac{60}{10-I} = \frac{60}{5}\) = 12 Ω.
9. The current flowing through the resistance R in the circuit in the figure has the form 2 cos 4t, where R is ____________
a) (0.18 + j0.72)
b) (0.46 + j1.90)
c) – (0.18 + j1.90)
d) (0.23 – 0.35 j)
View Answer
Explanation: Inductor is not given, hence ignoring the inductance. Let I1 and I2 are currents in the loop then,
I1 = \(\frac{2 cos4t}{3}\)
= 0.66 cos 4t
Again, I2 = \(\frac{-j X 4 X 0.75 I_1}{3.92-2.56j}\)
= (0.23 – 0.35j) cos 4t
10. In the circuit given below, the voltage VAB is _________
a) 6 V
b) 25 V
c) 10 V
d) 40 V
View Answer
Explanation: For finding the Thevenin Equivalent circuit across A-B we remove the 5 Ω resistor.
Then, I = \(\frac{10+50}{15}\) = 4 A
VOC = 50 – (10×4) =10 V
And REQ = \(\frac{10×5}{10+5} = \frac{10}{3}\) Ω
Current I1 = \(\frac{10}{10/3+5} = \frac{6}{5}\)
Hence, VAB = \(\frac{6}{5 × 5}\) = 6 V.
11. In the circuit given below, the magnitudes of VL and VC are twice that of VK. Calculate the inductance of the coil, given that f = 50.50 Hz.
a) 6.41 mH
b) 5.30 mH
c) 3.18 mH
d) 2.31 mH
View Answer
Explanation: VL = VC = 2 VR
∴ Q = \(\frac{V_L}{V_R}\) = 2
But we know, Q = \(\frac{ωL}{R} = \frac{1}{ωCR}\)
∴ 2 = \(\frac{2πf × L}{5}\)
Or, L = 3.18 mH.
12. In the circuit given below, the current source is 1 A, voltage source is 5 V, R1 = R2 = R3 = 1 Ω, L1 = L2 = L3 = 1 H, C1 = C2 = 1 F. The current through R3 is _________
a) 1 A
b) 5 A
c) 6 A
d) 8 A
View Answer
Explanation: At steady state, the circuit becomes,
∴ The current through R3 = \(\frac{5}{1}\) = 5 A.
13. In the circuit given below, the capacitor is initially having a charge of 10 C. 1 second after the switch is closed, the current in the circuit is ________
a) 14.7 A
b) 18.5 A
c) 40.0 A
d) 50.0 A
View Answer
Explanation: Using KVL, 100 = \(R\frac{dq}{dt} + \frac{q}{C}\)
100 C = \(RC\frac{dq}{dt}\) + q
Or, \(\int_{q_o}^q \frac{dq}{100C-q} = \frac{1}{RC} ∫_0^t \,dt\)
100C – q = (100C – qo)e-t/RC
I = \(\frac{dq}{dt} = \frac{(100C – q_o)}{RC} e^{-1/1}\)
∴ e-t/RC = 40e-1 = 14.7 A.
14. A circuit is given in the figure below. The Norton equivalent as viewed from terminals x and x’ is ___________
a) 6 Ω and 1.333 A
b) 6 Ω and 0.833 A
c) 32 Ω and 0.156 A
d) 32 Ω and 0.25 A
View Answer
Explanation: We, draw the Norton equivalent of the left side of xx’ and source transformed right side of yy’.
Vxx’ = VN = \(\frac{\frac{4}{8} + \frac{8}{24}}{\frac{1}{8} + \frac{1}{24}}\) = 5V
∴ RN = 8 || (16 + 8)
= \(\frac{8×24}{8+24}\) = 6 Ω
∴ IN = \(\frac{V_N}{R_N} = \frac{5}{6}\) = 0.833 A.
15. In the circuit given below, the current source is 1 A, voltage source is 5 V, R1 = R2 = R3 = 1 Ω, L1 = L2 = L3 = 1 H, C1 = C2 = 1 F. The current through the voltage source V is _________
a) 1 A
b) 3 A
c) 2 A
d) 4 A
View Answer
Explanation: At steady state, the circuit becomes,
∴ The current through the voltage source V = 5 – 1 = 4 A.
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