Question

A 100 $\Omega$ resistor, a 50 $\mu$F capacitor and an inductor are connected in series to an ac source of frequency 50 Hz. If the circuit is in resonance, then the impedance of the circuit is:

• A. 100 $\Omega$
• B. 200 $\Omega$
• C. 180 $\Omega$
• D. 250 $\Omega$

Hint:

At resonance in an RLC series circuit, impedance equals resistance ($Z = R$), as $X_L = X_C$, canceling out the reactive components.

Answer 1

The Correct Option is A

At resonance in an RLC series circuit, the inductive reactance $X_L$ equals the capacitive reactance $X_C$, so $X_L - X_C = 0$.
The impedance $Z$ of the circuit is then purely resistive: $Z = R$.
Given: $R = 100$ $\Omega$.
Thus, at resonance, $Z = 100$ $\Omega$.