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(C) The instantaneous voltage is given by $V = V_0 \cos \omega t$.For a purely resistive circuit,the root mean square $(RMS)$ voltage is $V_{rms} = \f

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$\frac{V_0^2}{2 R}$

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(C) The instantaneous voltage is given by $V = V_0 \cos \omega t$.For a purely resistive circuit,the root mean square $(RMS)$ voltage is $V_{rms} = \frac{V_0}{\sqrt{2}}$.The $RMS$ current is $I_{rms} = \frac{V_{rms}}{R} = \frac{V_0}{R \sqrt{2}}$.The average power dissipated in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$,where $\cos \phi$ is the power factor.For a resistor,the phase difference $\phi$ between voltage and current is $0$,so $\cos \phi = 1$.Substituting the values,we get $P = \left( \frac{V_0}{\sqrt{2}} \right) \left( \frac{V_0}{R \sqrt{2}} \right) (1)$.Therefore,$P = \frac{V_0^2}{2R}$.

When a voltage $V = V_0 \cos \omega t$ is applied across a resistor of resistance $R$,the average power dissipated per cycle in the resistor is given by

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