Question

A series LCR circuit with \( L = \frac{100}{\pi} \) mH, \( C = \frac{10^{-3}}{\pi} \) F and \( R = 10 \, \Omega \) is connected across an AC source of 220 V, 50 Hz supply. The power factor of the circuit would be _____.

Answer 1

Correct Answer: 1

Given:
\(L = \frac{100}{\pi} \, \text{mH} = \frac{100}{\pi} \times 10^{-3} \, \text{H}, \, C = 10^{-3} \, \text{F}, \, R = 10 \, \Omega, \, f = 50 \, \text{Hz}.\)

The inductive reactance is given by:
\(X_L = 2\pi f L = 2\pi \times 50 \times \frac{100}{\pi} \times 10^{-3} = 10 \, \Omega.\)

The capacitive reactance is given by:
\(X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi \times 50 \times 10^{-3}} = 10 \, \Omega.\)

Since \(X_L = X_C\), the circuit is in resonance. Therefore, the impedance is:
\(Z = R = 10 \, \Omega.\)

\(\text{Power Factor} = \frac{R}{Z} = 1.\)

The Correct answer is: 1