Discussion
The a.c circuit exhibiting the phenomenon of resonance has/have the circuit element(s)
Answer: E
Resonance needs an inductor and capacitor.
Resonance in an a.c. circuit occurs at the frequency where the inductive reactance equals the capacitive reactance, \(X_{L} = X_{C}\), so that the two cancel: \(\omega_{0} = 1/\sqrt{LC}\). At that frequency the current in a series LCR circuit is a maximum. Both an inductor and a capacitor are needed, because the effect comes from energy passing back and forth between the magnetic field of one and the electric field of the other.
A circuit with only an inductor, only a capacitor, or either one with a resistor has a single kind of reactance and nothing to cancel it, so it cannot resonate. A resistor is not needed for resonance; it only limits the peak current and sets the sharpness of the resonance.
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