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(B) The average power dissipated in an $a.c.$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$.Here,$V_{rms} = \varepsilon$ and $I_{rms} = \frac{\v

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$\frac{\varepsilon^2 R}{R^2 + (L\omega - \frac{1}{C\omega})^2}$

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(B) The average power dissipated in an $a.c.$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$.Here,$V_{rms} = \varepsilon$ and $I_{rms} = \frac{\varepsilon}{Z}$,where $Z$ is the impedance of the $LCR$ circuit.The power factor is $\cos \phi = \frac{R}{Z}$.Substituting these into the power formula:$P = \varepsilon \cdot \left( \frac{\varepsilon}{Z} \right) \cdot \left( \frac{R}{Z} \right) = \frac{\varepsilon^2 R}{Z^2}$.The impedance $Z$ of an $LCR$ series circuit is $Z = \sqrt{R^2 + (L\omega - \frac{1}{C\omega})^2}$.Therefore,$Z^2 = R^2 + (L\omega - \frac{1}{C\omega})^2$.Substituting $Z^2$ into the power equation,we get:$P = \frac{\varepsilon^2 R}{R^2 + (L\omega - \frac{1}{C\omega})^2}$.

Power dissipated in an $LCR$ series circuit connected to an $a.c.$ source of electromotive force (emf) $\varepsilon$ is:

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