When an RLC series circuit is connected to a 120 V rms, 60 Hz line, the rms curr

Question

When an RLC series circuit is connected to a 120 V rms, 60 Hz line, the rms current in the circuit is 11 A and this current leads the line voltage by 45 degrees. (a) Find the average power supplied to the circuit. (b) What is the resistance in the circuit? (c) If the inductance in the circuit is 50 mH, find the capacitance in the circuit. (d) Without changing the inductance, by how much should you change the capacitance to make the power factor equal to 1? (e) Without changing the capacitance, by how much should you change the inductance to make the power factor equal to 1?

Explanation / Answer

a) P = 120*11*cos(45) = 933 watts b) R = P/I^2 = 933/11^2 = 7.71 ohms c) Z = V/I = (120/_0)/(11/_45) = 10.91/_-45 = 7.71 - j7.71 ohms X = -j7.71 ohms XL = 2*pi*60*0.05 = j18.85 ohms -j7.71 = j18.85 - j/(2*pi*60*C) 1/(2*pi*60*C) = 18.85 + 7.71 C = 1/((2*pi*60)(18.85 + 7.71)) C = 100 uF

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