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

) and i(t) = 6 cos(120πt+60o

), determine the average power, rms value of v(t),

and the power factor

Expert's answer

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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