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(B) The power dissipated in an $AC$ circuit is given by the formula $P = V_{rms} I_{rms} \cos 	heta$.In a pure resistor $R$,the phase difference betw

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$\frac{I_0^2 R}{2}$

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(B) The power dissipated in an $AC$ circuit is given by the formula $P = V_{rms} I_{rms} \cos 	heta$.In a pure resistor $R$,the phase difference between voltage and current is $	heta = 0^\circ$,so $\cos 	heta = 1$.However,for a general $LCR$ circuit,the power dissipated is $P = I_{rms}^2 R$.The relationship between the peak current $I_0$ and the root mean square current $I_{rms}$ is $I_{rms} = \frac{I_0}{\sqrt{2}}$.Substituting this into the power formula: $P = \left( \frac{I_0}{\sqrt{2}} ight)^2 R = \frac{I_0^2 R}{2}$.Since the power is dissipated only across the resistor,the phase angle $	heta$ between the total voltage and total current in the $LCR$ circuit does not affect the power dissipated in the resistor $R$ directly,as $P = I_{rms}^2 R$ is the standard form.

$A$ sinusoidal $AC$ current passes through a resistor of resistance $R$ in an $LCR$ series circuit. If the phase difference between the supplied voltage and the supplied current is $\theta$ and the peak value of the supplied current is $I_0$,then the power dissipated in the circuit is:

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