Question

In an $a.c$. circuit, the instantaneous e.m.f. and current are given by
$e =100 \, \sin \, 30 t $
$i = 20 \, \sin \left( 30 t - \frac{\pi}{4} \right)$
In one cycle of $a.c$., the average power consumed by the circuit and the wattless current are, respectively :

• A. 50, 10
• B. $\frac{1000}{\sqrt{2}} , 10$
• C. $\frac{50}{\sqrt{2}} , 10$
• D. 50 , 0

Answer 1

Answer: (B)

$P_{\text {av }}=E_{\text {rms }} I_{\text {rms }} \cos \phi$
$=\frac{100}{\sqrt{2}} \times \frac{20}{\sqrt{2}} \times \frac{1}{\sqrt{2}}=\frac{1000}{\sqrt{2}}$
$i_{\text {wattless }}=i_{\text{ rms }} \sin \phi=\frac{20}{\sqrt{2}} \times \frac{1}{\sqrt{2}}=10$