Question

A simple circuit consists only of of a 1.0-μF capacitor and a 15-mH coil in series. At what frequency does the inductive reactance equal the capacitive reactance? 67 Hz 0.77 kHz 15 kHz 1.3 kHz

Answer 1

The frequency is 1.3 kHz.

Step-by-step explanation:

Given that,

Capacitance of the capacitor,
`C=1\ \mu F=10^(-6)\ C`

Inductance of the inductor,
`L=15\ mH=15* 10^(-3)\ H`

We need to find the frequency when the inductive reactance equal the capacitive reactance such that :

`X_c=X_L`

`2\pi fL=(1)/(2\pi fC)`

`f=(1)/(2\pi √(LC) )`

`f=\frac{1}{2\pi \sqrt{15* 10^(-3)* 10^(-6)} }`

f = 1299.49 Hz

`f=1.29* 10^3\ Hz`

or

`f=1.3\ kHz`

So, the frequency is 1.3 kHz. Therefore, the correct option is (d).