Question

The voltage applied to a circuit is v=100 sin(wt+30 º) and current flowing in the circuit is i= 15 sin(wt+60 º). induced emf. Determine: 1. Impedance 2.Phase angle between voltage and current 3.Active Power 4.Power Factor.

Answer 1

Gives

$V=100sin(wt+30°)$

$I=15sin(wt+60°)$

Impedance (Z)

$Z\sqrt{R^2+{(X_L-X_c})^2}$

$X_L=X_c=0$

Then

Z=R=$\frac{100}{15}=6.66\Omega$

Phase difference

$$∆\phi=(wt+60-wt+30)=30°$$

Active power

$P=\frac{IV}{2}cos\phi$

Put value

$P=\frac{100\times15}{2}cos30°$

P=650 W

Power factor

$Cos\phi =\frac{R}{Z}$

$R=\frac{V}{I}$

$R=\frac{100}{15}$

$Cos\phi=\frac{6.66}{6.66}=1$

$\phi=cos^{-1}1=0°$

Power factor$\phi=0°$