In an AC circuit containing an ideal inductor of inductance L connected to an AC source V = V₀ sin(ωt), what is the phase relationship between the current and the applied voltage?
Answer and explanation
Correct answer: C. Current lags behind voltage by π/2 radians (90°)
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- Step 1: In a purely inductive AC circuit, the voltage equation across the inductor is: .
- Step 2: Integrate to find current :
- Step 3: Letting , we have .
- Step 4: Comparing phase angles: the phase of voltage is and the phase of current is .
- Step 5: Therefore, the current lags behind the applied voltage by radians ().
Answer
Current lags behind voltage by π/2 radians (90°)
Why not the others: 'Current leads voltage by π/2' occurs in a purely capacitive circuit; 'Current and voltage are strictly in phase' occurs in a purely resistive circuit or a series LCR circuit at resonance; 'Current lags behind voltage by π' occurs in anti-phase configurations.
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