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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=5.0H$$C=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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