Question

In an a. c. circuit, the instantaneous e.m.f. and current are given by $e=100sin30t$
$i=20sin(30t-r/4)$. In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively.

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

Answer 1

The correct option is D $\frac{1000}{\sqrt{2}},10$

$e=100\sin 30t$
$i=20\sin (30t-\frac{\pi }{4})$
$P_{av}=e_{rms}{i}_{rms}\cos \varphi$
$=\frac{100}{\sqrt{2}}\cdot \frac{20}{\sqrt{2}}\cdot \frac{1}{\sqrt{2}}=\frac{1000}{\sqrt{2}}W$
Wattless current
$=\frac{I_0\sin \varphi }{\sqrt{2}}=\frac{20}{\sqrt{2}}\cdot \frac{1}{\sqrt{2}}=10A$