In an ac circuit,the instantaneous values of | vedclass

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(C) The given equations are $e = 200 \sin(314t)$ and $i = \sin(314t + \frac{\pi}{3})$.Comparing these with the standard forms $e = E_0 \sin(\omega t)$

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$50$

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(C) The given equations are $e = 200 \sin(314t)$ and $i = \sin(314t + \frac{\pi}{3})$.Comparing these with the standard forms $e = E_0 \sin(\omega t)$ and $i = I_0 \sin(\omega t + \phi)$,we get peak values $E_0 = 200 	ext{ V}$ and $I_0 = 1 	ext{ A}$,and phase difference $\phi = \frac{\pi}{3}$.The root mean square values are $V_{rms} = \frac{E_0}{\sqrt{2}} = \frac{200}{\sqrt{2}} 	ext{ V}$ and $I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{1}{\sqrt{2}} 	ext{ A}$.The average power consumed is given by $P = V_{rms} I_{rms} \cos \phi$.Substituting the values: $P = \left(\frac{200}{\sqrt{2}}ight) \left(\frac{1}{\sqrt{2}}ight) \cos(\frac{\pi}{3})$.Since $\cos(\frac{\pi}{3}) = 0.5$,we have $P = \frac{200}{2} 	imes 0.5 = 100 	imes 0.5 = 50 	ext{ W}$.

In an $ac$ circuit,the instantaneous values of e.m.f. and current are $e = 200 \sin(314t) \text{ V}$ and $i = \sin(314t + \frac{\pi}{3}) \text{ A}$. The average power consumed in watt is

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