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

Answer:

The value of the inductance is 175.9 mH.

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

$I_{rms}\times X_{L}=I_{rms}\times X_{C}$

$X_{L}=X_{C}$

$2\pi f L=\dfrac{1}{2\pi f C}$

$L=\dfrac{1}{4\pi^2\times f^2\times C}$

Put the value into the formula

$L=\dfrac{1}{4\times\pi^2\times60.0^2\times40\times10^{-6}}$

$L=0.1759\ H$

$L=175.9\times10^{-3}\ H$

$L=175.9\ mH$

Hence, The value of the inductance is 175.9 mH.