Question

A series ac circuit contains a 350-Ω resistor, a 11.0-mH inductor, a 3.70-μF capacitor, and an ac power source of voltage amplitude 45.0 V operating at an angular frequency of 360 rad/s . What is the power factor of this circuit? Find the average power delivered to the entire circuit. What is the average power delivered to the resistor, to the capacitor, and to the inductor? Enter your answers numerically separated by commas.

Answer 1

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X_c = 1/wc = 1/360*3.70e-6 = 750.75 ohms

X_L = wL = 3.96 ohms

(a) Power factor

cos = cos (tan^-1 ( X_L - X_C / R )

cos = 0.42437

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I_rms = V_rms / Z

Z = 824.74 ohms

V_rms = V/sqrt(2) = 31.819 V

therefore

I_rms = 31.819 V / 824.74 ohms

I_rms = 0.038581619 A

P =  0.038581619 A * 31.819*0.42437

P = 0.5209 W

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P_R = 0.5209 W

P_L = 0

P_C = 0