An RLC circuit with R = 24.4 , L = 325 mH, and C = 41.0 µF is connected to an ac

Question

An RLC circuit with R = 24.4 , L = 325 mH, and C = 41.0 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

b. twice the resonance frequency

c. half the resonance frequency

I solved part a. When I solve for part b with twice the frequency found, I get the wrong answer. I get the correct answer for b and c when they are both equal and I use half the frequency. Why is this?

Explanation / Answer

The key equations are

= 1/sqrt(LC) = 2pi*f

Pav = (Vrms2/Z2)*R

(a) At resonance, Z = R. Thus:

Pav = (Vrms2/R) = 24^2/24.4 = 23.6 W

b) Using = 2/sqrt(LC) = 2pi*f

gives Pav = (Vrms2/Z2)*R = (Vrms2*R)/(R^2 + [L - (1/C)]^2)

= (Vrms2*R)/(R^2 + [(2L/sqrt(LC)) - (sqrt(LC/2C)]^2)

=  (Vrms2*R)/(R^2 + (2*sqrt(L/C)) - 0.5(sqrt(L/C)^2)

= 24^2*24.4/[24.4^2 + (9*0.325/4*41*10^-6)] = 14054.4/18430.73 = 0.763 W

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