Please show all work and explain. To prevent incorrect answers I have used the p

Question

Please show all work and explain. To prevent incorrect answers I have used the practice numbers so that we can quickly see if the response is correct. The correct answer is 193V.

An RLC circuit is connected to a AC power supply. The amplitude of the power supply is 180.0V. To determine the maximum voltage across any element of the circuit one must determine the frequency at which it occurs. For the resistor, it is the resonance frequency. But what about the inductor or capacitor? Determine the maximum amplitude of the voltage across the inductor if R=90.0 ohms, C=3.96F, and L=25.0mH. The correct answer is 193V.

Explanation / Answer

at resonance w = 1/ sqrt(LC) = 1/sqrt(3.96*10^-6 *0.025)

w = 3178.2

again at resosnace impedence Z= R

so current i = V/Z = 180/90 = 2 A

now Xc = 1/wC = 1/ )(3178.2*3.96*10^-6) = 79.45 ohms

Xl =w L = 3178.2*0.025 = 79.455 ohms

so V across capacitor Vc = iXC = 2* 79.45 = 159 volts

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