(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 Electric 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

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Electric Potential and Capacitance

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Sharing of Charge in Capacitor Circuit

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$A$ capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system:

MediumNEET 2017

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Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12\, \mu C$ and $-3\, \mu C$ charges,respectively,and are at a large distance from each other. They are now connected by a conducting wire. $A$ long time after this is done,the charges on $S_{1}$ and $S_{2}$ are respectively:

DifficultJEE MAIN 2020

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$A$ capacitor of capacitance $C$ charged by an amount $Q$ is connected in parallel with an uncharged capacitor of capacitance $2C$. The final charges on the capacitors are

DifficultKCET 2019

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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

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$A$ capacitor of capacitance $50 \; pF$ is charged by a $100 \; V$ source. It is then connected to another uncharged identical capacitor. The electrostatic energy loss in the process is $\dots \; nJ$.

Two metal spheres of capacitance $C_1$ and $C_2$ carry some charges. They are put in contact and then separated. The final charges $Q_1$ and $Q_2$ on them will satisfy

$A$ capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system:

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