$A$ $10\ \mu F$ capacitor is charged to a potential difference of $1000\ V$. The terminals of the charged capacitor are disconnected from the power supply and connected to the terminals of an uncharged $6\ \mu F$ capacitor. What is the final potential difference across each capacitor in $V$?

$A$ $5\, \mu F$ capacitor is charged fully by a $220\,V$ supply. It is then disconnected from the supply and is connected in series to another uncharged $2.5\, \mu F$ capacitor. If the energy change during the charge redistribution is $\frac{ X }{100} \, J$,then the value of $X$ to the nearest integer is $.....$

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

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$. The switch $S_1$ is pressed first to fully charge the capacitor $C_1$ and then released. The switch $S_2$ is then pressed to charge the capacitor $C_2$. After some time, $S_2$ is released and then $S_3$ is pressed. After some time, which of the following statements are correct?

$A$ parallel plate capacitor of capacitance $C$ is connected to a battery and charged to a potential difference $V$. Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$. The charging batteries are then removed,and the capacitors are connected in parallel such that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is:

$A$ capacitor of $4\,\mu F$ charged to $50\,V$ is connected to another capacitor of $2\,\mu F$ charged to $100\,V$ with plates of like charges connected together. The total energy before and after connection in multiples of $10^{-2}\,J$ is: