A series RCL circuit contains a 5.05-?F capacitor and a generator whose voltage

Question

A series RCL circuit contains a 5.05-?F capacitor and a generator whose voltage is 12.4 V. At a resonant frequency of 1.30 kHz the power dissipated in the circuit is 27.6 W. Find the values of (a) the inductance and (b) the resistance. (c) Calculate the power factor when the generator frequency is 2.60 kHz. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

Explanation / Answer

1/sqrt(LC) = 2*(22/7)*1300 =>L = 0.0029656 = 2.9656mH P = V^2/R = 27.6 =>R = (12.4^2)/27.6 = 5.571014493 If f = 2600Hz w = (2*(22/7)*2600) =>Z = sqrt((5.571014493^2)+((((2*(22/7)*2600)*0.0029656)-(1/((2*(22/7)*2600)*5.05*(10^(-6)))))^2)) = 36.77421341 Power factor = R/Z = 0.151492418

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