In a series LCR circuit, the alternating e.m. | vedclass

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(D) The average power dissipated in an $AC$ circuit is given by the formula: $P_{avg} = V_{rms} I_{rms} \cos \phi$. Here, $V_{rms} = \frac{V_0}{\sqrt{

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$\frac{V_0 I_0}{4}$

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(D) The average power dissipated in an $AC$ circuit is given by the formula: $P_{avg} = V_{rms} I_{rms} \cos \phi$. Here, $V_{rms} = \frac{V_0}{\sqrt{2}}$ and $I_{rms} = \frac{I_0}{\sqrt{2}}$. The phase difference $\phi$ between the voltage and current is $\frac{\pi}{3}$ (or $60^{\circ}$). Substituting these values into the formula: $P_{avg} = \left(\frac{V_0}{\sqrt{2}}ight) \left(\frac{I_0}{\sqrt{2}}ight) \cos 60^{\circ}$. $P_{avg} = \frac{V_0 I_0}{2} 	imes 0.5$. $P_{avg} = \frac{V_0 I_0}{2} 	imes \frac{1}{2} = \frac{V_0 I_0}{4}$.

In a series $LCR$ circuit, the alternating e.m.f. and current are given by the equations $V = V_0 \sin(\omega t)$ and $I = I_0 \sin(\omega t + \frac{\pi}{3})$ respectively. The average power dissipated in the circuit over one cycle of a.c. is $(\cos 60^{\circ} = 0.5)$.

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