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Figure shows a series LCR circuit connected to a variable frequency 230 V source. Determine the source frequency which drives the circuit in resonance.

Q7.11     Figure shows a series LCR circuit connected to a variable frequency $230\: V$ source.  $L=5.0H$$C=80\mu F$, $R=40\Omega$.

(a)    Determine the source frequency which drives the circuit in resonance.

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Given,

Variable frequency supply voltage $V$ = 230V

Inductance $L=5.0H$

Capacitance $C=80\mu F=80*10^{-6}F$

Resistance $R=40\Omega$

a) Resonance angular frequency in this circuit is given by :

$w_{resonance}=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{5*80*10^{-6}}}=\frac{1000}{20}=50rad/sec$

Hence this circuit will be in resonance when supply frequency is 50 rad/sec.

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