Problem: Consider a series RLC circuit. The applied voltage has a maximum value

Question

Problem: Consider a series RLC circuit. The applied voltage has a maximum value of 120 V and oscillates at a frequency of 81 Hz.

Part a: assume the circuit contains a variable capacitor, an 820 ohm resistor, and a 3.7 H inductor. Determine the value of the capacitor such that the voltage across the capacitor is out of phase with the applied voltage by 54 degree.

Part b: assume the circuit contains a variable inductor, an 820 ohm resistor, and a 1.5 microfarad capacitor. Determine the value of the inductance such that the voltage across the capacitor is out of phase with the applied voltage by 48 degree, which V(max) leading V(c).

Since they are kind of similar, I will just put what I thought I was supposed to do for part a:

using tan(theta) = (Xc - Xl)/R; I solved for the capacitance. This didn't come out correctly, and I tried it many ways, so I am assuming this is the wrong formula. Can you help me please?

Explanation / Answer

a ) In series RLC circuit maximum applied voltage is V = 120 V frequency is   f = 81 Hz inductor is L = 3.7 H resistance R = 820 tan = ( L - 1/ C / R) tan 54 = ( 2fL - 1 / 2f C / R )              = (2*81 Hz * 3.7 H - 1/ 2*81Hz * C ) / 820         Capaxcitor is C = 2.609*10^-6 F b ) tan = ( L - 1/ C / R)       tan 48 = ( L - 1.31*10^3 F ) / 820       L = 1.79 H

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