In a series LCR circuit,an alternating emf (v | vedclass

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(B) The average power dissipated in an $AC$ circuit is given by the formula $P_{avg} = v_{rms} i_{rms} \cos \phi$.Given the equations for emf $v = v_{

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$ \frac{v_{0} i_{0}}{4} $

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(B) The average power dissipated in an $AC$ circuit is given by the formula $P_{avg} = v_{rms} i_{rms} \cos \phi$.Given the equations for emf $v = v_{0} \sin \omega t$ and current $i = i_{0} \sin \left(\omega t + \frac{\pi}{3}ight)$,the phase difference is $\phi = \frac{\pi}{3}$.The root mean square values are $v_{rms} = \frac{v_{0}}{\sqrt{2}}$ and $i_{rms} = \frac{i_{0}}{\sqrt{2}}$.Substituting these values into the power formula:$P_{avg} = \left(\frac{v_{0}}{\sqrt{2}}ight) \left(\frac{i_{0}}{\sqrt{2}}ight) \cos \left(\frac{\pi}{3}ight)$$P_{avg} = \frac{v_{0} i_{0}}{2} 	imes \frac{1}{2}$$P_{avg} = \frac{v_{0} i_{0}}{4}$.

In a series $LCR$ circuit,an alternating emf $(v)$ and current $(i)$ are given by the equations $v = v_{0} \sin \omega t$ and $i = i_{0} \sin \left(\omega t + \frac{\pi}{3}\right)$. The average power dissipated in the circuit over a cycle of $AC$ is:

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