an lrc circuit has ( l = 14.8 mathrm{mh} ) and ( r = 7.30 omega ).
part a
what value must ( c ) have to produce resonance at ( 4600 mathrm{~hz} ) ?
express your answer to three significant figures and include the appropriate units.
( c = )

Question

Accepted Answer

# Explanation:
## Step1: Recall the resonance formula
At resonance, $ \omega = \frac{1}{\sqrt{LC}} $, and $ \omega = 2\pi f $. So $ 2\pi f=\frac{1}{\sqrt{LC}} $, then $ C=\frac{1}{4\pi^{2}f^{2}L} $.
## Step2: Convert units
Given $ L = 14.8\space mH=14.8\times10^{- 3}\space H $, $ f = 4600\space Hz $.
## Step3: Substitute values into the formula
$$
\begin{align*}
C&=\frac{1}{4\pi^{2}(4600)^{2}(14.8\times 10^{-3})}\
&=\frac{1}{4\times(3.14)^{2}\times4600^{2}\times14.8\times 10^{-3}}\
\end{align*}
$$
$$
\begin{align*}
4\times(3.14)^{2}\times4600^{2}\times14.8\times 10^{-3}&=4\times9.8596\times21160000\times14.8\times 10^{-3}\
&=39.4384\times21160000\times14.8\times 10^{-3}\
&=834, 416, 544\times14.8\times 10^{-3}\
&=12459364.85\times10^{-3}\
& = 12459.36485
\end{align*}
$$
$ C=\frac{1}{12459.36485}\approx8.03\times10^{-6}\space F = 8.03\space\mu F $

# Answer:
$8.03\space\mu F$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the resonance formula

Step2: Convert units

Step3: Substitute values into the formula

Answer: