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  4. Figure shows a series LCR circuit connected to a variable frequency 230 V source. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/f0e55cada411c1e2e4865574a5fa3ccb-.jpeg /> The source frequency which drives the circuit in resonance is

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Q. Figure shows a series $LCR$ circuit connected to a variable frequency $230\,V$ source.
image
The source frequency which drives the circuit in resonance is

Alternating Current

Solution:

Here, $L = 5\,H$,
$C= 80\,\mu F = 80 \times 10^{-6}\,F$,
$R = 40\,\Omega$
$V_{rms}=230\,V$
The resonant angular frequency is
$ \omega_{r}=\frac{1}{\sqrt{LC}}$
$=\frac{1}{\sqrt{5\times80\times10^{-6}}}$
$=50\,rad\,s^{-1}$
$\therefore \upsilon_{r}=\frac{\omega}{2\pi}$
$=\frac{50}{2\pi}$
$8\,Hz$