Answer to Question #143946 in Electrical Engineering for ali

Question #143946
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
1
Expert's answer
2020-11-13T10:51:20-0500

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


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