Question

If v(t) = 10 cos(120πt+30o
) and i(t) = 6 cos(120πt+60o
), determine the average power, rms value of v(t),
and the power factor

Answer 1

Given $v(t) = 10\cos(120\pi t+30\degree)$

Given $i(t) =6\cos(120\pi t+60)$

$Vrms=\frac{10}{\sqrt2}=7.071V$ (rms value of $v(t).$

$Irms = \frac{6}{\sqrt2}= 4.243A$

Phase difference between current and voltage $(\phi)=60-30=30\degree lead$

Powerfactor$=\cos\phi=\cos30=0.866 \space lead$

Average power$=Vrms\times Irms\times\cos\phi=7.071\times 4.243\times0.866= 25.98\space W$