Question

A 40.0-μFcapacitor is connected across a 60.0 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?

Answer 1

The value of the inductance is 175.9 mH.

Step-by-step explanation:

Given that,

Capacitor
`C= 40.0\ \muF`

Frequency = 60.0 Hz

The inductor and capacitor is connected in parallel, the voltage across each of these elements is the same.

We have,

`V_(L)=V_(C)`

Using ohm's law

`I_(rms)* X_(L)=I_(rms)* X_(C)`

`X_(L)=X_(C)`

`2\pi f L=(1)/(2\pi f C)`

`L=(1)/(4\pi^2* f^2* C)`

Put the value into the formula

`L=(1)/(4*\pi^2*60.0^2*40*10^(-6))`

`L=0.1759\ H`

`L=175.9*10^(-3)\ H`

`L=175.9\ mH`

Hence, The value of the inductance is 175.9 mH.