This set of Network Theory Objective Questions & Answers focuses on “Advanced Problems on Application of Laplace Transform – 2”.

1. A capacitor of 110 V, 50 Hz is needed for AC supply. The peak voltage of the capacitor should be ____________

a) 110 V

b) 460 V

c) 220 V

d) 230 V

View Answer

Explanation: We know that,

Peak voltage rating = 2 (rms voltage rating).

Given that, rms voltage rating = 110 V

So, Peak voltage rating = 110 X 2 V

= 220 V.

2. Given I (t) = 10[1 + sin (- t)]. The RMS value of I(t) is ____________

a) 10

b) 5

c) \(\sqrt{150}\)

d) 105

View Answer

Explanation: Given that, I (t) = 10[1 + sin (- t)]

Now, RMS value = \(\sqrt{10^2 + \frac{10^2}{\sqrt{2}}}\)

= \(\sqrt{100+50}\)

= \(\sqrt{150}\).

3. A two branch parallel circuit has a 50 Ω resistance and 10 H inductance in one branch and a 1 μF capacitor in the second branch. It is fed from 220 V ac supply, at resonance, the input impedance of the circuit is _____________

a) 447.2 Ω

b) 500 Ω

c) 235.48 Ω

d) 325.64 Ω

View Answer

Explanation: We know that,

For a parallel resonance circuit impedance = \([\frac{L}{RC}]^{0.5}\)

Given, R = 50 Ω, L = 10 H and C = 1 μF

= \([\frac{10}{50*1}]^{0.5}\)

So, impedance = 447.2 Ω.

4. The impedance matrices of two, two-port network are given by [3 2; 2 3] and [15 5; 5 25]. The impedance matrix of the resulting two-port network when the two networks are connected in series is ____________

a) [3 5; 2 25]

b) [18 7; 7 28]

c) [15 2; 5 3]

d) Indeterminate

View Answer

Explanation: Given that two impedance matrices are [3 2; 2 3] and [15 5; 5 25]. Here, the resulting impedance is the sum of the two given impedances.

So resulting impedance = [18 7; 7 28].

5. The electrical energy required to heat a bucket of water to a certain temperature is 10 kWh. If heat losses, are 10%, the energy input is ____________

a) 2.67 kWh

b) 3 kWh

c) 2.5 kWh

d) 3.5 kWh

View Answer

Explanation: Given that, 10% of input is lost.

So, 0.90 Input = 10

Or, Input = \(\frac{10}{0.9}\) = 11.11 kWh.

6. The current rating of a cable depends on ___________

a) Length of the cable

b) Diameter of the cable

c) Both length and diameter of the cable

d) Neither length nor diameter of the cable

View Answer

Explanation: We know that Current rating depends only on the area of cross-section. Since the area of cross section is a function of radius, which in turn is a function of diameter, so the current rating depends only on the Diameter of the cable.

7. In an AC circuit, the maximum and minimum values of power factor can be ___________

a) 2 and 0

b) 1 and 0

c) 0 and -1

d) 1 and -1

View Answer

Explanation: We know that, power factor is maximum and equal to 1 for a purely resistive load. Power factor is minimum and equal to zero for a purely reactive load.

Hence, in an AC circuit, the maximum and minimum values of power factor are 1 and 0 respectively.

8. In the circuit given below, the series circuit shown in figure, for series resonance, the value of the coupling coefficient, K will be?

a) 0.25

b) 0.5

c) 0.1

d) 1

View Answer

Explanation: Mutual inductance w

_{m}= ω k \(\sqrt{L_1 L_2}\)

Or, m = k.2.8 j

^{2}

= 4k.j

At resonance, Z = 20 – j10 + j2 + j6 + 2.4kj – 2j + 8kj = 0

Or, -2 = -8k

Or, k = \(\frac{1}{4}\) = 0.25.

9. In an RC series circuit R = 100 Ω and X_{C} = 10 Ω. Which of the following is possible?

a) The current and voltage are in phase

b) The current leads the voltage by about 6°

c) The current leads the voltage by about 84°

d) The current lags the voltage by about 6°

View Answer

Explanation: In RC circuit the current leads the voltage.

Or, θ = tan

^{-1}\(\frac{10}{100}\)

This is nearly equal to 6°

Hence, the current lags the voltage by about 6°.

10. The impedance of an RC series circuit is 12 Ω at f = 50 Hz. At f = 200 Hz, the impedance will be?

a) More than 12

b) Less than 3

c) More than 3 Ω but less than 12 Ω

d) More than 12 Ω but less than 24 Ω

View Answer

Explanation: We know that the impedance Z, is given by

Z = R

^{2}+ \(X_C^2\)

When f is made four times, X

_{C}becomes one-fourth but R remains the same.

So, the impedance is more than 3 Ω but less than 12 Ω.

11. A 3 phase balanced supply feeds a 3-phase unbalanced load. Power supplied to the load can be measured by ___________

a) 2 Wattmeter and 1 Wattmeter

b) 2 Wattmeter and 3 Wattmeter

c) 2 Wattmeter and 2 Wattmeter

d) Only 3 Wattmeter

View Answer

Explanation: We know that, a minimum of 2 wattmeters is required to measure a 3-phase power. Also, power can be measured by using only one wattmeter in each phase. Hence, power supplied to the load can be measured by 2 Wattmeter and 3 Wattmeter methods.

12. A series RC circuit has R = 15 Ω and C = 1 μF. The current in the circuit is 5 sin 10t. The applied voltage is _____________

a) 218200 cos (10t – 89.99°)

b) 218200 sin (10t – 89.99°)

c) 218200 sin (10t)

d) 218200 cos (10t)

View Answer

Explanation: Given that, R = 15Ω, X

_{C}= \(\frac{1}{ωC}\)

= \(\frac{10^6}{10 X 1}\) = 10

^{5}Ω

Now, θ = tan

^{-1}\(\frac{X_C}{R}\) = 89.99°

We know that, impedance Z is given by,

Z = \(\sqrt{R^2 + X_C^2}\) = 10

^{2}kΩ.

Hence, V = 100000(2.182).sin(10 t – 89.99°)

Or, V = 218200 sin (10t – 89.99°).

13. A capacitor stores 0.15C at 5 V. Its capacitance is ____________

a) 0.75 F

b) 0.75 μF

c) 0.03 F

d) 0.03 μF

View Answer

Explanation: We know that, Q = CV

Given, V = 5 V, Q = 0.15 C

Hence, 0.15 = C(5)

Or, C = 0.03 F.

14. For a transmission line, open circuit and short circuit impedances are 10 Ω and 20 Ω. Then characteristic impedance is ____________

a) 100 Ω

b) 50 Ω

c) 25 Ω

d) 200 Ω

View Answer

Explanation: We know that, the characteristic impedance Z0 is given by,

Z

_{0}= Z

_{oc}Z

_{sc}

Given that, open circuit impedance, Z

_{oc}= 10 Ω and short circuit impedance, Z

_{sc}= 20 Ω.

So, Z

_{0}= (10.20) Ω

= 200 Ω.

15. A circuit excited by voltage V has a resistance R which is in series with an inductor and a capacitor 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, Z

_{DY}= \(\frac{L}{R_LC}\)

But given that R

_{L}= 0

So, Z

_{DY}= \(\frac{L}{0XC}\) = ∞

Therefore current through the circuit, I = \(\frac{V}{∞}\) = 0

∴ V

_{D}= 0.

**Sanfoundry Global Education & Learning Series – Network Theory.**

To practice all objective questions on Network Theory, __here is complete set of 1000+ Multiple Choice Questions and Answers__.

**If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]**

**Related Posts:**

- Check Electronics & Communication Engineering Books
- Apply for Electronics & Communication Engineering Internship
- Practice Electrical Engineering MCQs
- Apply for Electrical Engineering Internship
- Check Network Theory Books