In an a.c. circuit the e.m.f. (e) and the current (i ) at any instant are given respectively by…
In an a.c. circuit the e.m.f. (e) and the current (i ) at any instant are given respectively by
$\begin{aligned}
& e=E_0 \sin \omega t \\
& i=I_0 \sin (\omega t-\phi)
\end{aligned}$
The average power in the circuit over one cycle of a.c. is
$\mathrm{E}_0 \mathrm{I}_0$
$\frac{E_0 I_0}{2}$
$\frac{E_0 I_0}{2} \sin \phi$
$\frac{E_0 l_0}{2} \cos \phi$
Solution
Since phase difference between current and e.m.f is $\phi$
$\therefore P_{a V}=\frac{E_0 l_0}{2} \cos \phi$