Question

In an AC circuit, the instantanceous emf and current are given by
e=100 sin 30 t, i=sin(30 t $\frac{\pi }{4}$)
In one cycle of AC, the average power consumed by the circuit and the wattles current are, respectively

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

Answer 1

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

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

$=\left(\frac{V_0}{\sqrt{2}}\right)\left(\frac{I_0}{\sqrt{2}}\right)\cos \theta$

$=\left(\frac{100}{\sqrt{2}}\right)\left(\frac{20}{\sqrt{2}}\right)\cos {45}^o$

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

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

$=\frac{I_0}{\sqrt{2}}\sin \theta$

$=\frac{20}{\sqrt{2}}\sin {45}^o$

$=10$ amp.