Chapter 21, Problem 67P

To determine

The resonant frequency

Answer to Problem 67P

Solution:

The resonant frequency will be $3.63\times {10}^5\text{Hz}$

Explanation of Solution

Given:

$\begin{array}{l}L=55.0\text{μH}\\ C=3500\text{pF}\\ R=4.0\text{Ω}\end{array}$

Formula used:

$f_0=\frac{1}{2\pi }\sqrt{\frac{1}{LC}}$

Where,

$\begin{array}{l}L=55.0\text{μH}\\ C=3500\text{pF}\\ R=4.0\text{Ω}\end{array}$

Calculation:

$f_0=\frac{1}{2\pi }\sqrt{\frac{1}{LC}}$

$f_0=\frac{1}{2\pi }\sqrt{\frac{1}{LC}}=\frac{1}{2\pi }\sqrt{\frac{1}{4{\pi }^2{\left(55.0\times {10}^{-6}\text{H}\right)}^2\left(3500\times {10}^{-12}\text{F}\right)}}=3.63\times {10}^5\text{Hz}$