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  4. The frequency at which the inductive reactance of 2H inductance will be equal to the capacitive reactance of 2 μ F capacitance (nearly)

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Q. The frequency at which the inductive reactance of 2H inductance will be equal to the capacitive reactance of $2 \mu F$ capacitance (nearly)

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Solution:

$X _{ L }= X _{ C }$
$W L =\frac{1}{ WC }$
$W ^{2}=\frac{1}{ LC }$
$W =\sqrt{\frac{1}{ LC }}$
$f =\frac{1}{2 \pi} \sqrt{\frac{1}{ LC }}$
$=\frac{1}{2 \pi} \sqrt{\frac{1}{2 \times 2 \times 10^{-6}}}$
$=\frac{1}{2 \pi} \times \frac{1}{2 \times 10^{-3}}$
$=\frac{10^{3}}{4 \pi}$
$ =80\,Hz$