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  • Figure shows a series LCR circuit connected to a variable frequency 230 V source. Show that the potential drop across the LC combination is zero at the resonating frequency.

Q7.11(c) Figure shows a series LCR circuit connected to a variable frequency 230\: V source. Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.(\text{where,}\ L=5H, C=80\mu F \ \text{and} R=40\Omega)

           

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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

Now, According to the series RLC circuit, the rms potential drop across the inductor is given by

 I_{rms}*(impedance)

I_{rms}=\frac{I_{peak}}{\sqrt{2}}=\frac{8.13}{\sqrt{2}}=5.85A

Now, Potential drop across the capacitor,

V_{capacitor}=I_{rms}*\left (\frac{1}{w_{resonance}C} \right ) =5.85*\left ( \frac{1}{50*80*10^{-6}} \right )=1437.5V

Potential drop across the inductor,

V_{inductor}=I_{rms}*(w_{resonance}L) =5.85* 50*5=1437.5V

The potential drop across the Resistor,

V_{resistor}=I_{rms}*\R =5.85* 40=230V

The potential drop across LC combination

V_{LC}=I_{rms}*\left ( wL-\frac{1}{wC} \right )=5.85*0=0

Hence, it is proved that the potential drop across the LC combination is zero at resonating frequency.

Posted by

Pankaj Sanodiya

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