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(D) The instantaneous power in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$,where $\phi$ is the phase difference between voltage and cu

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(D) The instantaneous power in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$,where $\phi$ is the phase difference between voltage and current.Given voltage $V = 200 \sin(100t)$ and current $i = 5 \sin(100t - \frac{\pi}{2})$.The phase of voltage is $\phi_V = 100t$ and the phase of current is $\phi_i = 100t - \frac{\pi}{2}$.The phase difference $\phi = \phi_V - \phi_i = 100t - (100t - \frac{\pi}{2}) = \frac{\pi}{2}$.The power consumption is $P = V_{rms} I_{rms} \cos(\frac{\pi}{2})$.Since $\cos(\frac{\pi}{2}) = 0$,the power consumption $P = 0 	ext{ W}$.

In an $AC$ circuit,the current is given by $i = 5 \sin(100t - \frac{\pi}{2}) \text{ A}$ and the $AC$ potential is $V = 200 \sin(100t) \text{ V}$. Then the power consumption is $....$ watt.

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