(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

Two capacitors $C_1$ and $C_2 = 2C_1$ are connected with a switch $S$ as shown in the figure. Initially,the switch is open and the charge on capacitor $C_1$ is $Q$. Now,when the switch is closed,the final charges on the capacitors are:

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Two metallic spheres of radii $1 \, cm$ and $3 \, cm$ are given,with charges of $-1 \times 10^{-2} \, C$ and $5 \times 10^{-2} \, C$ respectively. If these are connected by a conducting wire,the final charge on the bigger sphere is

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Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. When they are brought into contact with each other:

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Two spheres of radii $R_1$ and $R_2$ have the same initial charge $q$. They are connected by a copper wire. After they are disconnected,the potential of each sphere is $V$. What was the initial charge $q$ on each sphere?

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$A$ capacitor of $20\,\mu F$ is charged to $500\,V$ and connected in parallel with another capacitor of $10\,\mu F$ which is charged to $200\,V$. The common potential is.......$V$.

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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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Two capacitors $C_1$ and $C_2 = 2C_1$ are connected with a switch $S$ as shown in the figure. Initially,the switch is open and the charge on capacitor $C_1$ is $Q$. Now,when the switch is closed,the final charges on the capacitors are:

Two metallic spheres of radii $1 \, cm$ and $3 \, cm$ are given,with charges of $-1 \times 10^{-2} \, C$ and $5 \times 10^{-2} \, C$ respectively. If these are connected by a conducting wire,the final charge on the bigger sphere is

Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. When they are brought into contact with each other:

Two spheres of radii $R_1$ and $R_2$ have the same initial charge $q$. They are connected by a copper wire. After they are disconnected,the potential of each sphere is $V$. What was the initial charge $q$ on each sphere?

$A$ capacitor of $20\,\mu F$ is charged to $500\,V$ and connected in parallel with another capacitor of $10\,\mu F$ which is charged to $200\,V$. The common potential is.......$V$.

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