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.

            

Answers (1)

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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