Question

For an LRC series circuit containing a resistance of 1 1.0 kQ, a capacitance of 2.0 μF and an inductance of 24.0 H, what frequency is needed to maximize the current? A) 144 Hz B) 1,700 Hz C) 10,000 kHz D) 23 Hz E) 350 Hz

Answer 1

(D) 23 Hz

Step-by-step explanation:

We have given resistance
`R=11kohm=11* 10^3ohm`

Inductance L =24 H

Capacitance
`C=2\mu F=2* 10^(-6)F`

We have to maximize the current so we need minimum impedance which is possible in case of resonance

In resonance condition
`X_L=X_C`

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

`\omega =(1)/(√(LC))`

`f =(1)/(2\pi √(LC))`

`f =\frac{1}{2* 3.14\sqrt{24* 2* 10^(-6)}}=22.98Hz=23Hz`

So option (D) is correct option