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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

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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=XL-XC=ωL-1ωC
If ωL=1ωC, X = 0. So, the circuit contains an inductor and a capacitor.

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

(c) Similarly, for a circuit without an inductor, reactance is given by,
X''=XC=1ωC, which also cannot be zero.

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

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