(D) Let the capacitance of the air-cored capacitor be $C$. Then the capacitance of the capacitor with dielectric $K$ is $C_K = KC$.When connected,the

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(D) Let the capacitance of the air-cored capacitor be $C$. Then the capacitance of the capacitor with dielectric $K$ is $C_K = KC$.When connected,the total charge $Q = C \times V + KC \times 0 = CV$.The total capacitance of the system is $C_{total} = C + KC = C(1 + K)$.The common potential $V'$ is given by $V' = \frac{Q}{C_{total}} = \frac{CV}{C(1 + K)} = \frac{V}{1 + K}$.Rearranging for $K$: $1 + K = \frac{V}{V'}$.Therefore,$K = \frac{V}{V'} - 1 = \frac{V - V'}{V'}$.

Class 12 Physics Electrostatic Potential and Capacitance Sharing of Charge in Capacitor Circuit

Medium

An uncharged parallel plate capacitor having a dielectric of constant $K$ is connected to a similar air-cored parallel capacitor charged to a potential $V$. The two share the charge and the common potential is $V'$. The dielectric constant $K$ is

A
$\frac{V' - V}{V' + V}$
B
$\frac{V' - V}{V'}$
C
$\frac{V' - V}{V}$
D
$\frac{V - V'}{V'}$

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Class 12 Questions

Class 12

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Chapter

Electrostatic Potential and Capacitance

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Sharing of Charge in Capacitor Circuit

$A$ parallel plate capacitor of capacitance $500 \ pF$ is charged with a $100 \ V$ supply. It is then disconnected from the supply and connected to another uncharged $500 \ pF$ capacitor. The electrostatic energy lost in this process is (in $\mu J$)

MediumAP EAMCET 2022

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$A$ capacitor $C$ is fully charged with voltage $V_{0}$. After disconnecting the voltage source,it is connected in parallel with another uncharged capacitor of capacitance $\frac{C}{2}$. The energy loss in the process after the charge is distributed between the two capacitors is $.........$ $CV_{0}^{2}$.

DifficultJEE MAIN 2020

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$A$ $3\ \mu F$ capacitor is charged to a potential of $300\ V$ and a $2\ \mu F$ capacitor is charged to $200\ V$. They are then connected in parallel with plates of opposite polarity joined together. What is the amount of charge (in $\mu C$) that flows through the connecting wires?

Medium

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$A$ capacitor of capacitance $0.2 \, \mu F$ is charged to a potential of $600 \, V$. After removing the battery,it is connected in parallel to an uncharged capacitor of $1.0 \, \mu F$. The final potential across the capacitors will be.........$V$.

Medium

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$A$ capacitor of $10\,\mu F$ charged up to $250\,V$ is connected in parallel with another capacitor of $5\,\mu F$ charged up to $100\,V$. The common potential is.....$V$.

Medium

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An uncharged parallel plate capacitor having a dielectric of constant $K$ is connected to a similar air-cored parallel capacitor charged to a potential $V$. The two share the charge and the common potential is $V'$. The dielectric constant $K$ is

Similar Questions

$A$ parallel plate capacitor of capacitance $500 \ pF$ is charged with a $100 \ V$ supply. It is then disconnected from the supply and connected to another uncharged $500 \ pF$ capacitor. The electrostatic energy lost in this process is (in $\mu J$)

$A$ $3\ \mu F$ capacitor is charged to a potential of $300\ V$ and a $2\ \mu F$ capacitor is charged to $200\ V$. They are then connected in parallel with plates of opposite polarity joined together. What is the amount of charge (in $\mu C$) that flows through the connecting wires?

$A$ capacitor of capacitance $0.2 \, \mu F$ is charged to a potential of $600 \, V$. After removing the battery,it is connected in parallel to an uncharged capacitor of $1.0 \, \mu F$. The final potential across the capacitors will be.........$V$.

$A$ capacitor of $10\,\mu F$ charged up to $250\,V$ is connected in parallel with another capacitor of $5\,\mu F$ charged up to $100\,V$. The common potential is.....$V$.

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