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 wattles 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 $\frac{1000}{\sqrt{2}},10$

$P_{a}vg=V_{rms}{I}_{rms}\cos \theta$

$=\left(\frac{V_o}{\sqrt{2}}\right)\left(\frac{I_o}{\sqrt{2}}\right)cos\theta$

$=\left(\frac{100}{\sqrt{2}}\right)\left(\frac{20}{\sqrt{2}}\right)cos45$

$=\frac{1000}{\sqrt{2}}watt$

Wattless current = $I_{rms}sin\theta$

= $\frac{I_o}{\sqrt{2}}sin\theta$

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

= $10amp$