In a series R-L-C AC circuit,for a particular | vedclass

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(D) At resonance in a series $R-L-C$ circuit,the inductive reactance $X_L$ equals the capacitive reactance $X_C$ $(X_L = X_C)$.The impedance of the ci

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$P = P'$

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(D) At resonance in a series $R-L-C$ circuit,the inductive reactance $X_L$ equals the capacitive reactance $X_C$ $(X_L = X_C)$.The impedance of the circuit is purely resistive,$Z = R$.The power supplied by the source at resonance is given by $P = \frac{V^2}{R}$,where $V$ is the root-mean-square voltage of the source.Since the power $P$ depends only on the voltage $V$ and the resistance $R$,it is independent of the values of $L$ and $C$ as long as the circuit is at resonance.When the inductance $L$ is halved,the resonance condition can still be met by adjusting the frequency of the source (or the capacitance $C$).At the new resonance condition,the impedance remains $Z' = R$.Therefore,the new power $P'$ is also $P' = \frac{V^2}{R}$.Comparing the two,we get $P = P'$.

In a series $R-L-C$ $AC$ circuit,for a particular value of $R, L$ and $C$,the power supplied by the source is $P$ at resonance. If the value of inductance is halved,then the power from the source again at resonance is $P'$. Then:

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