Question

#1A 41.2-µF capacitor is connected across a 55.8-Hz generator. An inductor is then connected in parallel with the capacitor. What is the value of the inductance if the rms currents in the inductor and capacitor are equal?

_____ mH

#2

A 39.0-mH inductor has a reactance of 1.90 kΩ.

What is the capacitance of a capacitor that has the same reactance at this frequency?
___F

please help me and show me how to do the work correctly

Answer 1

1.

if rms currents in inductor and capacitor are equal means Capacitive reactance is equal capacitive reactance

X_L=X_C

2pifL=1/2pifC

=>L=1/4pi²f²C =1/4pi²*55.8²*(41.2*10^-6)

L=197.5 mH

2.

from inductive reactance is given by

X_L=WL

=>W=X_L/L=(1.9*10³)/(39*10^-3)

W=48718 rad/sec

Capacitive reactance is given by

X_C=1/WC

=>C=1/WX_c=1/48718*1.9*10³

C=1.08*10^-8 F