Question

An engineer has a 37.0 µH inductor, a 37.0 µF capacitor, and a variable frequency AC source. Determine the source frequency (in kHz) at which the inductor and capacitor have the same reactance.

Answer 1

Frequency will be 4.30 kHz

Step-by-step explanation:

We have inductance
`L=37\mu H=37* 10^(-6)H`

And capacitance
`C=37\mu H=37* 10^(-6)F`

Inductive reactance is given by
`X_L=\omega L`

And capacitive reactance
`X_C=(1)/(\omega C)`

As in question it is given that inductive reactance and capacitive reactance is same

So
`X_L=X_C`

`\omega L=(1)/(\omega C)`

`\omega ^2=\sqrt{(1)/(LC)}=\frac{1}{\sqrt{37* 10^(-6)* 37* 10^(-6)}}=27027.027rad/sec`

We know that angular frequency
`\omega =2\pi f`

`2* 3.14* f=27027.027`

f = 4303.66 Hz =4.30 kHz