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

#### Solution

(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)