Question

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 an inductor nor a capacitor

Answer 1

(a) an inductor and a capacitor
(d) neither an inductor nor a capacitor

(a) The reactance of a circuit containing a capacitor and an inductor is given by,
$X=X_L-X_C=\omega L-\frac{1}{\omega C}$
If $\omega L=\frac{1}{\omega C}$, X = 0. So, the circuit contains an inductor and a capacitor.

(b) For a circuit without a capacitor, reactance is given by,
$X^{\text{'}}=X_L=\omega L$, which cannot be zero for an AC source.

(c) Similarly, for a circuit without an inductor, reactance is given by,
$X^{\text{'}\text{'}}=X_C=\frac{1}{\omega C}$, which also cannot be zero.

(d) For a circuit without any capacitor and inductor, reactance, X^' = 0 ( L = C = 0)