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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    Figure shows a series LCR circuit connected to a variable frequency 230\: V source.

                L=5.0HC=80\mu F, R=40\Omega.

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.

            

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Potential difference across any element = I_{rms}*(impedance)

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

NOW,

The potential difference across 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 difference across the inductor 

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

The potential difference across Resistor 

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

Potential difference across LC combination

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

Hence at resonating frequency potential difference across LC combination is zero.

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