An ideal 043H inductor and a capacitor are connected in seri

An ideal 0.43-H inductor and a capacitor are connected in series with an ideal 60-Hz generator. A digital voltmeter is used to measure the rms voltages across the inductor and capacitor independently. The voltmeter reading across the capacitor is 86 V and that across the inductor is 54 V. Find the capacitance and the rms current in the circuit. What is the rms voltage across the series combination of the capacitor and the inductor?

Solution

a)

Voltage across the inductor, VL = 54 V

So, current in the inductor, I = Vl/XL = 54/(2*pi*f*L)

So, I = 54/(2*pi*600.43)

= 0.0143 A

So, current in the capacitor, I = 0.0143 A

So, 0.0143 = Vc/(Xc)

So, 0.0143 = 86/(1/(2*pi*60*C))

So, C = 4.41*19^-7 F = 0.441 u F <----answer

b)

rms current in the circuit = I = 0.0143 A = 14.3 mA <---- found in previous part

c)

rms volrage across the series combination:

Vrms = 86 - 54 V = 32 V