Question

In an a.c. circuit, the instantaneous e.m.f. and current are given by
$e=100\sin 30t$
$i=20\sin (30t-\frac{\pi }{4})$
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. $\frac{50}{\sqrt{2}},0$
• D. $50,0$

Answer 1

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

Given,

$e=100sin30t$

$i=20sin(30t-\frac{\pi }{4})$

The average power consumed by the circuit is,

$P_{avg}=e_{rms}.i_{rms}cos\varphi$

$P_{rms}=\frac{e_0}{\sqrt{2}}.\frac{i_0}{\sqrt{2}}cos\frac{\pi }{4}$

$P_{avg}=\frac{100}{\sqrt{2}}.\frac{20}{\sqrt{2}}cos45$

$P_{avg}=\frac{1000}{\sqrt{2}}$. . . . .(1)

The wattless current, $I=i_{rms}sin\varphi$

$I=\frac{i_0}{\sqrt{2}}sin\frac{\pi }{4}$

$I=\frac{20}{\sqrt{2}}sin45$

$I=10A$

The correct option is B.