(A) Initial energy $E_0 = \frac{1}{2} C_0 V_0^2$. Case $(i)$: Battery is disconnected. Charge $Q = C_0 V_0$ remains constant. When separation $d$ is d

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(A) Initial energy $E_0 = \frac{1}{2} C_0 V_0^2$. Case $(i)$: Battery is disconnected. Charge $Q = C_0 V_0$ remains constant. When separation $d$ is doubled,new capacitance $C' = C_0/2$. Energy $E_1 = \frac{Q^2}{2C'} = \frac{(C_0 V_0)^2}{2(C_0/2)} = C_0 V_0^2 = 2E_0$. Case $(ii)$: Battery remains connected. Potential $V_0$ remains constant. When separation $d$ is doubled,new capacitance $C' = C_0/2$. Energy $E_2 = \frac{1}{2} C' V_0^2 = \frac{1}{2} (C_0/2) V_0^2 = \frac{1}{4} C_0 V_0^2 = E_0/2$. Therefore,$E_1/E_2 = (2E_0) / (E_0/2) = 4$.

Class 12 Physics Electrostatic Potential and Capacitance Mix Examples - Electric Potential and Capacitance

Medium

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$.
$(i)$ The energy stored in the capacitor when the battery is disconnected and the separation is doubled is $E_1$.
$(ii)$ The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$.
Then the value of $E_1/E_2$ is:

A
$4$
B
$1.5$
C
$2$
D
$0.25$

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Electrostatic Potential and Capacitance

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Mix Examples - Electric Potential and Capacitance

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by the above two particles will be:

MediumJEE MAIN 2022

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Plates $A$ and $B$ constitute an isolated,charged parallel-plate capacitor. The inner surfaces ($I$ and $IV$) of $A$ and $B$ have charges $+Q$ and $-Q$ respectively. $A$ third plate $C$ with charge $+Q$ is now introduced midway between $A$ and $B$. Which of the following statements is not correct?

Medium

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$A$ $1\,\mu F$ capacitor is connected in the circuit shown below. The $EMF$ of the cell is $3\,V$ and its internal resistance is $0.5\,\Omega$. The resistors $R_1$ and $R_2$ have values $4\,\Omega$ and $1\,\Omega$ respectively. The charge on the capacitor in steady state is.......$\mu C$.

Medium

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Five capacitors of $10\,\mu F$ capacity each are connected to a $d.c.$ potential of $100\;V$ as shown in the figure. The equivalent capacitance between the points $A$ and $B$ will be equal to..........$\mu F$.

Medium

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If the potential of $A$ is $10\,V$,then the potential of $B$ is

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An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by the above two particles will be:

Plates $A$ and $B$ constitute an isolated,charged parallel-plate capacitor. The inner surfaces ($I$ and $IV$) of $A$ and $B$ have charges $+Q$ and $-Q$ respectively. $A$ third plate $C$ with charge $+Q$ is now introduced midway between $A$ and $B$. Which of the following statements is not correct?

$A$ $1\,\mu F$ capacitor is connected in the circuit shown below. The $EMF$ of the cell is $3\,V$ and its internal resistance is $0.5\,\Omega$. The resistors $R_1$ and $R_2$ have values $4\,\Omega$ and $1\,\Omega$ respectively. The charge on the capacitor in steady state is.......$\mu C$.

Five capacitors of $10\,\mu F$ capacity each are connected to a $d.c.$ potential of $100\;V$ as shown in the figure. The equivalent capacitance between the points $A$ and $B$ will be equal to..........$\mu F$.

If the potential of $A$ is $10\,V$,then the potential of $B$ is

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