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 = omegaL - 1/(omegaC)`
if `omegaL = 1/(omegaC)  X = 0`. so , the circuit contains an inductor and a capacitor.

(b) For a circuit without a capacitor, reactance is given by, 
`X' = X_L = omegaL` which cannot be zero for an AC source.

(c) Similarly, for a circuit without an inductor, reactance is given by,
X" = `Xc = 1/(omega C)`

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