Question

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

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