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(B) The instantaneous values are given by $e = E_0 \sin(\omega t)$ and $I = I_0 \sin(\omega t + \phi)$.Comparing with the given equations,$E_0 = 10

Vedclass · Accepted Answer

$25$

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(B) The instantaneous values are given by $e = E_0 \sin(\omega t)$ and $I = I_0 \sin(\omega t + \phi)$.Comparing with the given equations,$E_0 = 10 	ext{ V}$,$I_0 = 10 	ext{ A}$,and the phase difference $\phi = \frac{\pi}{3}$.The average power consumed in an $A.C.$ circuit is given by $P_{	ext{avg}} = V_{	ext{rms}} I_{	ext{rms}} \cos \phi$.We know that $V_{	ext{rms}} = \frac{E_0}{\sqrt{2}}$ and $I_{	ext{rms}} = \frac{I_0}{\sqrt{2}}$.Substituting these values: $P_{	ext{avg}} = \left(\frac{10}{\sqrt{2}}ight) 	imes \left(\frac{10}{\sqrt{2}}ight) 	imes \cos\left(\frac{\pi}{3}ight)$.$P_{	ext{avg}} = \left(\frac{100}{2}ight) 	imes \frac{1}{2} = 50 	imes 0.5 = 25 	ext{ W}$.

In an $A.C.$ circuit,the instantaneous values of $\text{e.m.f}.$ and current are $e = 10 \sin(50 \pi t) \text{ V}$ and $I = 10 \sin(50 \pi t + \frac{\pi}{3}) \text{ A}$. The average power consumed in the circuit is $... \text{ W}$.

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