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 (in watts) and the wattless current (in amperes) are respectively (Assume SI units)

• 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 $\frac{1000}{\sqrt{2}},10$

Average power consumed by the circuit
$P_{\text{avg}}=V_{\text{rms}}.I_{\text{rms}}.\cos \varphi$
$P_{\text{avg}}=\frac{100}{\sqrt{2}}.\frac{20}{\sqrt{2}}.\cos {45}^{\circ }$
$P_{\text{avg}}=\frac{1000}{\sqrt{2}}\text{W}$

Wattless current $=I_v\sin {45}^{\circ }$
$\therefore i_{\text{wattless}}=\frac{20}{\sqrt{2}}\times \sin {45}^{\circ }$
$=\frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=10A$