Physics Questions and Answers – AC Voltage Applied to a Capacitor

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This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “AC Voltage Applied to a Capacitor”.

1. A 1.5 μF capacitor is connected to a 220 V, 50 Hz source. Find the capacitive reactance in the circuit.
a) 2120 Ω
b) 21.2 Ω
c) 212 Ω
d) 2.12 Ω

Explanation: Xc = $$\frac {1}{2πfC}$$
Xc = $$\frac {1}{(2 \times 3.14 \times 50 \times 1.50 \times 10^{-6})}$$
Xc = 212 Ω

2. A capacitor of capacitance 10 μF is connected to an oscillator giving an output voltage, E = 10 sin ωt volt. If ω = 10 rad s-1, find the peak current in the circuit.
a) 197 mA
b) 1 mA
c) 179 mA
d) 5 mA

Explanation: I0 = $$\frac {E_0}{(\frac {1}{\omega C})}$$
I0 = ωCE0.
I0 = 10 × 10 × 10-6 × 10
I0 = 10-3A = 1 mA.

3. What is the capacitive reactance of a 5 μF capacitor when it is a part of a circuit whose frequency is 50 Hz?
a) 636.6 Ω
b) 1636.6 Ω
c) 2636.6 Ω
d) 4636.6 Ω

Explanation: Xc = $$\frac {1}{2πfC}$$
Xc = $$\frac {1}{(2 \times 3.14 \times 50 \times 5 \times 10^{-6})}$$
Xc = 636.6 Ω.
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4. How will the capacitive reactance be affected if the frequency is doubled?
a) Doubled
b) Insignificant
c) Remains the same
d) Halved

Explanation: If the frequency is doubled, the capacitive reactance is halved and consequently, the current is doubled. This is because, when capacitive reactance, being a resistance, is lowered, the current can flow more easily through the circuit.

5. Give the SI unit of capacitive reactance.
a) Am
b) Ω
c) Ωm
d) A

Explanation: Capacitive Reactance is the complex impedance of a capacitor whose value changes with respect to the applied frequency. The SI unit of capacitive reactance is the ohm (Ω). Capacitive reactance is denoted by Xc.

6. The capacitive reactance varies directly with the frequency.
a) True
b) False

Explanation: Xc = $$\frac {1}{\omega_C}$$
Xc = $$\frac {1}{2πfC}$$.
Thus the capacitive reactance varies inversely with the frequency. Therefore as frequency increases, the capacitive reactance decreases.

7. Calculate the rms value of current in the circuit wherein an 80 μF capacitor is connected to a 100 V, 80 Hz ac supply.
a) 4 A
b) 2 A
c) 7 A
d) 50 A

Explanation: Xc = $$\frac {1}{2πfC}$$
Xc = $$\frac {1}{(2 \times 3.14 \times 80 \times 80 \times 10^{-6})}$$
Xc = 24.8 Ω.
Irms = $$\frac {E_{rms}}{X_C}$$
Irms = $$\frac {100}{24.8}$$
Irms = 4.03 A ≈ 4 A.

8. What will be the reactance of a capacitor at 150 Hz, if it has a reactance of 200 Ω at 50 Hz?
a) 67 Ω
b) 40 Ω
c) 150 Ω
d) 60 Ω

Explanation: $$\frac {X_C^{’}}{X_C} =\frac {f}{f^{’}}$$
Xc = $$\frac {(50 \times 200)}{(150)}$$
Xc = 66.7 Ω ≈ 67 Ω
Therefore, the reactance at 150 Hz will be 67 Ω.

9. A 1.50 μF capacitor is connected to a 220 V, 50 Hz source. If the frequency is doubled, what happens to the capacitive reactance?
a) Remains the same
b) Doubled
c) Halved
d) Becomes zero

Explanation: When the frequency is doubled, the capacitive reactance will be halved. This is because the capacitive reactance (Xc) is inversely proportional to the frequency (f). This is the effect of capacitive reactance on frequency.

10. Which among the following is the correct expression for finding capacitive reactance for an ac circuit containing capacitor only?
a) Xc = 2πf
b) Xc = $$\frac {1}{2πfC}$$
c) Xc = 2πfC
d) Xc = $$\frac {2πf}{C}$$

Explanation: For an ac circuit containing capacitor only,
Xc = $$\frac {1}{\omega_C}$$
Xc = $$\frac {1}{2πfC}$$.

Sanfoundry Global Education & Learning Series – Physics – Class 12.

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