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

Answer:

(e)$6.835\times 10^{-7}F$

Explanation:

At resonance we know that $X_l=X_C$

That is $\omega L=\frac{1}{\omega C}$

$\omega ^2=\frac{1}{LC}$

$\omega =\frac{1}{\sqrt{LC}}$

$f=\frac{1}{2\pi \sqrt{LC}}$

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

So $4511=\frac{1}{2\pi \sqrt{LC}}$

$LC=\frac{1}{4\pi ^2\times 4511^2}$

$LC=1.244\times 10^{-9}$

$C=\frac{1.244\times 10^{-9}}{1.82\times 10^{-3}}=0.6835\times 10^{-6}=6.835\times 10^{-7}F$

So option e is the correct answer