Question 11 Mark
The instantaneous magnitudes of current and voltage in an ac circuit are given as $I =10 \sin 314 t A$ and $V =50 \sin \left(314 t +\frac{\pi}{2}\right) \quad V$ respectively. What is the dissipation of average power in the circuit?
Answer
View full question & answer→Phase difference between voltage and current $=\frac{\pi}{2}$
$\therefore \quad \cos \phi=\cos \frac{\pi}{2}=0$
$\therefore \quad$ Average power $\quad \begin{aligned}
\overline{\mathrm{P}} =\mathrm{V}_{\mathrm{rms}} \mathrm{I}_{\mathrm{rms}} \cos \phi \\ =\mathrm{V}_{\mathrm{rms}} \times \mathrm{I}_{\mathrm{rms}} \times 0=0\end{aligned}$
$\therefore \quad \cos \phi=\cos \frac{\pi}{2}=0$
$\therefore \quad$ Average power $\quad \begin{aligned}
\overline{\mathrm{P}} =\mathrm{V}_{\mathrm{rms}} \mathrm{I}_{\mathrm{rms}} \cos \phi \\ =\mathrm{V}_{\mathrm{rms}} \times \mathrm{I}_{\mathrm{rms}} \times 0=0\end{aligned}$
