Question

A circuit containing an inductor and a capacitor in series is designed to have a resonant frequency of 4511 Hz. If the inductor has inductance 1.82 mH, then what is the required capacitance of the capacitor? Select one: a. 8.3e-4 Farads b.0.12 Farads c. 6.8e-10 Farads d. 2.7e-5 Farads e. 6.8e-7 Farads

Answer 1

(e)
`6.835* 10^(-7)F`

Step-by-step explanation:

At resonance we know that
`X_l=X_C`

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

`\omega ^2=(1)/(LC)`

`\omega =(1)/(√(LC))`

`f=(1)/(2\pi √(LC))`

We have given resonance frequency f =4511 Hz and inductance L=1.82 mH

So
`4511=(1)/(2\pi √(LC))`

`LC=(1)/(4\pi ^2* 4511^2)`

`LC=1.244* 10^(-9)`

`C=(1.244* 10^(-9))/(1.82* 10^(-3))=0.6835* 10^(-6)=6.835* 10^(-7)F`

So option e is the correct answer