# Multiple Choice Questions on Circuit Theory

1. Twelve 6 Ω resistor used as edge to form a cube. The resistance between two diagonally opposite corner of the cube is

The electric current i will be distributed in the cube branches symmetrically.

2. The energy required to charge a 10 μF capacitor to 100 V is

3. In the circuit of figure below a charge of 600 C is delivered to 100 V source in a 1 minute. The value of V1 must be

In order for 600 C charge to be delivered to 100 V source, the electric current must be anti-clockwise.

Applying KVL we get
V1 + 60 – 100 = 10 × 20 ⇒ V1 = 240 V

4. R1 = 36 Ω and R2 = 75 Ω, each having tolerance of ±5% are connected in series. The value of resultant resistance is

R1 = 36 ± 5% = 36 ± 1.8 Ω
R2 = 75 ± 5%=75 ± 3.75 Ω
∴ R1 + R2 = 111 ± 5.55 Ω

5. A particular electric current is made up of two component : a 10 A and a sine wave of peak value 14.14 A. The average value of electric current is

Average dc electric current = 10 A.
Average ac electric current = 0 A as it is alternating in nature.
Average electric current = 10 + 0 = 10 A.

6. In the circuit given below the value of resistance Req is

The circuit is as shown in figure below.

7. The switch S is the circuit shown in figure is ideal. If the switch is repeatedly closed for 1 ms and opened for 1 ms, the average value of i(t) is

Since i = 5 / (10 × 10-3)=0.5 × 10-3 = 0.5 mA
As the switch is repeatedly close, then i(t) will be a square wave.
So average value of electric current is ( 0.5 / 2 ) = 0.25 mA.

8. The linear circuit element is

A linear circuit element does not change their value with voltage or current.

9. Active element of electrical circuit is

Active elements are used to drive the circuit. They cause the electric current to flow through the circuit or the voltage drop across the element.

10. The basic circuit elements are

The elements, which show their behaviour only when they are excited, are called basic circuit element.

11. The energy stored in the magnetic field at a solenoid 30 cm long and 3 cm diameter wound with 1000 turns of wire carrying a electric current at 10 A, is

12. The resistance of a strip of copper of rectangular cross section is 2 Ω. A metal of resistivity twice that of a copper is coated on its upper surface to a thickness equal to that of copper strip. The resistance of composite strip will be

Copper and coated metal strip have resistance 2 ohms respectively. These two strips are in parallel.
Resistance of composite strip = (2 × 4) / ( 2 + 4 )= 4 / 3 ohms.

13. The two windings of a transformer have an inductor of 2 H each. If mutual inductor between them is also 2 H, then

14. The form factor of sinusoidal alternating electric current is

For alternating electric current form factor is defined as the ratio of rms value and average value of alternating current.
Now the rms value of alternating electric current = 0.07 × maximum value of alternating current.
Average value of alternating electric current = 0.637 × maximum value of alternating current.
So from factor = 0.707 / 0.637 = 1.11.

15. The rms value of sine wave is 100 A. Its peak value is

For sinusoidal alternating electric current the peak factor or amplitude factor can be expressed the ratio of maximum or peak value and rms value of alternating current.
So the peak value = rms value of alternating electric current × peak factor of alternating electric current = 100 × 1.414 = 141.4 A

16. Potential of earth is – 50 V. If potential difference between anode and cathode (earthed) is measured as 150 V, actual voltage on anode is

Actual voltage on anode, V = 150 – ( - 50 ) = 200 V

17. An alternating voltage e = 150sin314t is supplied to a device which offers a resistance of 20 Ω in forward direction of electric current while preventing the flow of electric current in reverse direction. Calculate the form factor.

From the voltage equation, we can get Vm = 150 V and Im = 150 / 20 = 7 A
RMS value of the current, Irms= Im / 2 = 7 /2 = 3.5 A
Average value of the current, Iavg = Im / π = 2.228 A
Form factor = Irms / Iavg = 3.5 / 2.228 = 1.57.

18. A coil of 300 turns is wound on a non-magnetic core having a mean circumference of 300 mm and a cross sectional area of 300 mm2. The inductor of the coil corresponding to a magnetizing electric current of 3 A will be

19. A network contains linear resistors and ideal voltage source s. If values of all the resistors are doubled, then voltage across each resistor is

V / R ratio is a constant R. If R is doubled then, electric current will become half. So voltage across each resistor is same.

20. A voltage waveform V(t) = 12t2 is applied across a 1 H inductor for t ≥ 0, with initial electric current through it being zero. The electric current through the inductor for t ≥ 0 is given by