Question

If a capacitor of 500 nF is connected to an AC source of frequency 1 kHz, then the capacitive reactance of the capacitor is

• A. \( \frac{10^3}{\pi}~\Omega \)
• B. \( \frac{10^4}{\pi}~\Omega \)
• C. \( 2 \times 10^3~\Omega \)
• D. \( \frac{\pi \times 10^3}{2}~\Omega \)

Hint:

To calculate capacitive reactance, remember: higher frequency or capacitance results in lower reactance.

Answer 1

The Correct Option is A

Capacitive reactance is given by: \[ X_C = \frac{1}{2\pi f C} \] Substitute values: \[ f = 1~\text{kHz} = 10^3~\text{Hz},\quad C = 500~\text{nF} = 500 \times 10^{-9}~\text{F} \] \[ X_C = \frac{1}{2\pi \times 10^3 \times 500 \times 10^{-9}} = \frac{1}{\pi \times 10^{-3}} = \frac{10^3}{\pi}~\Omega \]