The reactance of a circuit is zero. It is possible that the circuit contains:
A. an inductor and a capacitor
B. an inductor but no capacitor
C. a capacitor but no inductor
D. Neither inductor nor capacitor
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A & D Only
The reactance of an ac circuit comes from its inductor and capacitor. In a series circuit the net reactance is
\( \displaystyle X = X_L - X_C = \omega L - \frac{1}{\omega C} \)
(A) an inductor and a capacitor — Correct. At resonance, \( \omega = 1/\sqrt{LC} \), \( X_L = X_C \) and the net reactance is zero.
(B) an inductor but no capacitor — Incorrect. The reactance is \( X_L = \omega L \), which is not zero for an ac supply, and nothing cancels it.
(C) a capacitor but no inductor — Incorrect. The reactance is \( X_C = 1/(\omega C) \), which is not zero, and nothing cancels it.
(D) Neither inductor nor capacitor — Correct. A purely resistive circuit has no reactance at all.
NCERT (2026-27):
Resonance – “… So if \( \omega \) is varied, then at a particular frequency \( \omega_0 \), Xc = XL, and the impedance is minimum \( \left(Z = \sqrt{R^2 + 0^2} = R\right) \). This frequency is called the resonant frequency.”