Question

An alternating voltage of 220 V, 50 Hz frequency is applied across a capacitor of capacitance 2 μF. The impedance of the circuit is:

• A. \( \dfrac{\pi}{5000} \)
• B. \( 1000 \pi \)
• C. \( 500 \pi \)
• D. \( \dfrac{500}{\pi} \)

Hint:

For a capacitive circuit, the impedance is inversely proportional to both the frequency and the capacitance.

Answer 1

The Correct Option is C

Step 1: The impedance \( Z \) of a capacitive circuit is given by \( Z = \dfrac{1}{\omega C} \), where \( \omega = 2\pi f \) is the angular frequency, \( C \) is the capacitance, and \( f \) is the frequency.
Step 2: Given \( f = 50 \, \text{Hz} \) and \( C = 2 \, \mu \text{F} \), we calculate the impedance as: \[ Z = \dfrac{1}{2\pi \times 50 \times 2 \times 10^{-6}} = 500 \pi. \]
Final Answer: \[ \boxed{500 \pi} \]