$A$ $10\,\mu F$ capacitor is fully charged to a potential difference of $50\, V$. After removing the source voltage, it is connected to an uncharged capacitor in parallel. Now, the potential difference across them becomes $20\, V$. The capacitance of the second capacitor is $\dots \mu F$.

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

$A$ $5\, \mu F$ 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 $.....$

Consider the situation shown in the figure. The switch $S$ is kept open for a long time and then closed. Find the charge that flows through the battery when $S$ is closed.

$A$ body of capacity $4\,\mu F$ is charged to $80\,V$ and another body of capacity $6\,\mu F$ is charged to $30\,V$. When they are connected,the energy lost by the $4\,\mu F$ capacitor is.......$mJ$.

Two spheres $A$ and $B$ of radius $4\,cm$ and $6\,cm$ are given charges of $80\,\mu C$ and $40\,\mu C$ respectively. If they are connected by a fine wire,the amount of charge flowing from one to the other is