This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Problems Involving Coupling Coefficient”.

1. An RLC series circuit has a resistance R of 20Ω and a current which lags behind the applied voltage by 45°. If the voltage across the inductor is twice the voltage across the capacitor, the value of inductive resistance is ____________

a) 10 Ω

b) 20 Ω

c) 40 Ω

d) 60 Ω

2. In the Wheatstone bridge shown below, if the resistance in each arm is increased by 0.05%, then the value of V_{out} will be?

a) 50 mV

b) Zero

c) 5mV

d) 0.1mV

3. If the 3-phase balanced source in the given figure delivers 1500 W at a leading power factor of 0.844, then the value of Z_{L} is approximately __________

a) 90∠32.44°

b) 80∠32.44°

c) 80∠-32.44°

d) 90∠-32.44°

4. The voltage drop across a standard resistor of 0.2 Ω is balanced at 83 cm. The magnitude of the current, if the standard cell emf of 1.53 V is balanced at 42 m is ___________

a) 13.04 A

b) 10 A

c) 14.95 A

d) 12.56 A

5. The simultaneous applications of signals x (t) and y (t) to the horizontal and vertical plates respectively, of an oscilloscope, produce a vertical figure of 8 displays. If P and Q are constants and x(t) = P sin (4t + 30), then y(t) is equal to _________

a) Q sin (4t – 30)

b) Q sin (2t + 15)

c) Q sin (8t + 60)

d) Q sin (4t + 30)

6. A 200/1 Current Transformer (CT) is wound with 400 turns on the secondary on a toroidal core. When it carries a current of 180 A on the primary, the ratio is found to be -0.5%. If the number of secondary turns is reduced by 1, the new ratio error (in %) will be?

a) 0.0

b) -0.5

c) -1.0

d) -2.0

7. The readings of polar type potentiometer are

I = 12.4∠27.5°

V = 31.5∠38.4°

Then, Reactance of the coil will be?

a) 2.51 Ω

b) 2.56 Ω

c) 2.54 Ω

d) 2.59 Ω

8. A resistor of 10 kΩ with a tolerance of 5% is connected in parallel with 5 kΩ resistors of 10% tolerance. The tolerance limit is __________

a) 9%

b) 12.4%

c) 8.33%

d) 7.87%

9. In the Two wattmeter method of measuring power in a balanced three-phase circuit, one wattmeter shows zero and the other positive maximum. The load power factor is ___________

a) 0

b) 0.5

c) 0.866

d) 1.0

10. In the figure given below, a 220 V 50 Hz supplies a 3-phase balanced source. The pressure Coil (PC) and Current Coil (CC) of a watt-meter are connected to the load as shown. The watt-meter reading is _________

a) Zero

b) 1600 W

c) 242 W

d) 400 W

11. In Maxwell’s capacitance bridge for calculating unknown inductance, the various values at balance are, R_{1} = 300 Ω, R_{2} = 700 Ω, R_{3} = 1500 Ω, C_{4} = 0.8 μF. The values of R_{1}, L_{1} and Q factor, if the frequency is 1100 Hz are ____________

a) 240 Ω, 0.12 H, 3.14

b) 140 Ω, 0.168 H, 8.29

c) 140 Ω, 0.12 H, 5.92

d) 240 Ω, 0.36 H, 8.29

12. The meter constant of a single-phase, 230 V induction watt-meter is 600 rev/kW-h. The speed of the meter disc for a current of 15 A at 0.8 power factor lagging will be?

a) 30.3 rpm

b) 25.02 rpm

c) 27.6 rpm

d) 33.1 rpm

13. In the Owen’s bridge shown in below figure, Z_{1} = 200∠60°, Z_{2} = 400∠-90°, Z_{3} = 300∠0°, Z_{4} = 400∠30°. Then,

a) Bridge is balanced with given impedance values

b) Bridge can be balanced, if Z_{4} = 600∠60°

c) Bridge can be balanced, if Z_{3} = 400∠0°

d) Bridge cannot be balanced with the given configuration

14. In the figure below, the values of the resistance R_{1} and inductance L_{1} of a coil are to be calculated after the bridge is balanced. The values are _________________

a) 375 Ω and 75 mH

b) 75 Ω and 150 mH

c) 37.5 Ω and 75 mH

d) 75 Ω and 75 mH

15. The four arms of an AC bridge network are as follows:

Arm AB: unknown impedance

Arm BC: standard capacitor C_{2} of 1000pf

Arm CD: a non-inductive resistance of R of 100 Ω in parallel to a capacitor of 0.01 μF

Arm DA: a non-inductive resistance of 1000 Ω

The supply frequency is 50 Hz and connected across terminals B and D. If the bridge is balanced with the above value, determine the value of unknown Impedance.

a) 10 kΩ

b) 100 kΩ

c) 250 kΩ

d) 20 kΩ