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Alternating Current
Series LCR Circuit – Power Factor
1 question from 1 paper, each with its answer.
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- of Alternating Current
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Concepts tested
- power factor at resonance
All Questions
2020 1 question
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A series LCR circuit is connected to an ac voltage source. When $L$ is removed from the circuit, the phase difference between current and voltage is $\frac{\pi}{3}$. If instead $C$ is removed from the circuit, the phase difference is again $\frac{\pi}{3}$ between current and voltage. The power factor of the circuit is:When L is removed: $\tan\frac{\pi}{3} = \frac{X_C}{R}$ ...(i) When C is removed: $\tan\frac{\pi}{3} = \frac{X_L}{R}$ ...(ii) From (i) and (ii), $X_L = X_C$, so the circuit is at resonance and Z = R. Power factor $= \cos\phi = \frac{R}{Z} = 1$
