Power delivered by the ac source of the circu | vedclass

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Question

(B) In an $L-C-R$ series circuit,the power delivered by the $ac$ source is given by $P = V_{rms} I_{rms} \cos \phi$.The power factor $\cos \phi$ is ma

Vedclass · Accepted Answer

$\omega L = \frac{1}{\omega C}$

Vedclass · Answer

(B) In an $L-C-R$ series circuit,the power delivered by the $ac$ source is given by $P = V_{rms} I_{rms} \cos \phi$.The power factor $\cos \phi$ is maximum (equal to $1$) when the circuit is in resonance.At resonance,the inductive reactance $X_L$ is equal to the capacitive reactance $X_C$.Thus,$X_L = X_C$.Substituting the formulas for reactances,we get $\omega L = \frac{1}{\omega C}$.When this condition is met,the impedance $Z = \sqrt{R^2 + (X_L - X_C)^2}$ becomes minimum $(Z = R)$,which results in maximum current and maximum power delivered by the source.

Power delivered by the $ac$ source of the circuit becomes maximum when

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