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A resistance \( (\boldsymbol{R})=12 \Omega ; \) inductance \( (L)=2 \) henry and capacitive reactance \( C=5 m F \) are connected in series to an ac generator, then:

1. at resonance, the circuit impedance is zero
2. at resonance, the circuit impedance is \( 12 \Omega \)
3. the resonance frequency of the circuit is \( 1 / 2 \pi \)
4. at resonance, the inductive reactance is less than the capacitive reactance

Correct answer: at resonance, the circuit impedance is \( 12 \Omega \)

Solution

In a series RLC circuit at resonance, inductive and capacitive reactances are equal and opposite, so they cancel. The total impedance is then purely resistive, equal to R = 12 a9.

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