In a series LCR circuit, V_{L} = V_{C} ≠ V_{R}. What is the value of power factor?

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#### Solution

In an LCR series circuit, power dissipated is given by

P = I^{2}ZcosΦ

`P/(I^2sqrt(R^2+(X_C-X_L)^2))=cosphi`

The quantity cosΦ is the power factor.

`cosphi=P/(I^2sqrt(R^2+(X_C-X_L)^2))`

∵ V_{L}=V_{C} and X_{L}= X_{C}

`:.cosphi=P/(I^2R)`

Concept: Ac Voltage Applied to a Series Lcr Circuit

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