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  4. The resonant frequency of a series LCR circuit with L = 2.0 H, C = 32 μ F and R= 10 Ω is

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Q. The resonant frequency of a series $LCR$ circuit with $L = 2.0 \,H$, $C = 32\, \mu F$ and $R= 10\,\Omega$ is

Alternating Current

Solution:

Here, $L = 2\,H$,
$C= 32 \,\mu F = 32 \times 10^{-6}\,F$,
$R = 10\,\Omega$
$\therefore \omega_{r}=\frac{1}{\sqrt{LC}}$
$=\frac{1}{\sqrt{2\times32\times10^{-6}}}$
$=125\,rad\,s^{-1}$
$\upsilon_{r}=\frac{\omega_{r}}{2\pi}$
$=\frac{125}{2\times3.14}$
$=20\,Hz$