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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 = 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)
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