Question

A 13 Ω resistor is connected in series with a 360 mH inductor and a 1.6 µF capacitor. The applied voltage has the form V = V0 sin(2πf t), with voltage amplitude V0 = 497 V and frequency f = 1722 Hz . Find the effective voltage Vrms across the capacitor. Answer in units of V.

Answer 1

Vrms across the capacitor = i0*X_C/(2)^(1/2)= (v0/z)*X_C/(2)^(1/2)

where z = total impedence of the circuit = (R^2 + (X_C - XL)^2)^(1/2)

where X_C= 1/w*C = 1/2*pi*f*C = 1/(2*3.14*1722*1.6*10^-6 = 57.8 ohm

X_L = w*L = 2*pi*f*L = 2*3.14*1722*360*10^-3 = 3893.1 ohm

hence z = (169 + 14709507.68)^(1/2) = 3835.32 ohm

hence Vrms across the capacitor = (497/3835.32)*57.8/1.44 = 5.20 V