A 60 Hz 220 Vrms source supplies power to a load consisting of a resistance in s

Question

A 60 Hz 220 Vrms source supplies power to a load consisting of a resistance in series with a capacitance. The real power is 2000 W, and the apparent power is 2500 VA. Determine the value of the resistance and the value of the capacitance.

A 60 Hz 220 Vrms source supplies power to a load consisting of a resistance in series with a capacitance. The real power is 2000 W, and the apparent power is 2500 VA. Determine the value of the resistance and the value of the capacitance. Basically, the circuit looks like:

Explanation / Answer

    f = 60Hz, V=220V,   P =2000W,   S=2500 VA S = VI I = V/S = 220/2500 = 0.088 A P = S cos cos = P/S = 2000/2500 = 0.8 = cos-1 (0.8) = 37o P = I2 R R = P/I2 = 2000 /(0.088)2 R = 258k Q2 = S2 - P2 = (2500)2 - (2000)2 = 2250000 Q = 1500 VAR Q = I2 XC XC = Q/I2 = 1500/(0.088)2 = 194k XC = 1/2fC C = 1/(2)(3.14)(60)(194000) C = 13.7nF

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