Question

An RLC circuit with R = 24.6 ?, L = 325 mH, and C = 40.8 µF is connected to an ac generator with an rms voltage of 24 V. Determine the average power delivered to this circuit when the frequency of the generator is each of the following. (a) equal to the resonance frequency W (b) twice the resonance frequency W (c) half the resonance frequency W

Answer 1

Solution-

A) at resonance frequency,

XL = XC

Z = R

Irms = 24 / Z = 24 / 24.6=0.976 A


P = Irms^2 R =23.43 W

(B) w0 = 1 / sqrt(LC) = 1 / sqrt(0.325 x 40.8 x 10^-6)

= 274.62 rad/s

w = 2w0 = 549.23 rad/s

XL = w L = 178.49 ohm

Xc = 1 / wC = 44.62 ohm

Z = sqrt[ R^2 + (XL - XC)^2] = 136.11 ohm

Irms = 24 / 136.11 = 0.176 A


Pavh = 0.176^2 x 24.6 = 0.76 W

(C) w = w0 / 2 = 123.81 rad/s

XL = w L =40.24 ohm

Xc = 1 / wC = 197.96 ohm

Z = sqrt[ R^2 + (XL - XC)^2] = 159.63 ohm

Irms = 24 / 159.63 = 0.150 A


Pavh = 0.150^2 x 24.6 = 0.55 W