$A$ condenser having a capacity of $6\,\mu F$ is charged to $100\, V$ and is then joined to an uncharged condenser of $14\,\mu F$ and then removed. The ratio of the charges on $6\,\mu F$ and $14\,\mu F$ and the potential of $6\,\mu F$ will be

$A$ $10\,\mu F$ 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?......$V$

In the following figure,$C_1=5 \mu F$,$C_2=C_3=10 \mu F$ and $\varepsilon=20 \text{ V}$. Initially,the switch $S$ is connected to point $A$ until capacitor $C_1$ is fully charged. Afterwards,the switch is thrown to the left side and connected to point $B$. The charge on capacitor $C_3$ after equilibrium is reached will be (in $\mu C$)

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

The energy stored in the capacitor shown in figure $(a)$ is $4.5 \times 10^{-6} \ J$. If the battery is disconnected and the capacitor is connected to another uncharged capacitor of $900 \ pF$ as shown in figure $(b)$,what will be the total energy of the system?

$A$ $10 \mu F$ capacitor is charged by a $100 V$ battery. It is disconnected from the battery and is connected to another uncharged capacitor of capacitance $30 \mu F$. During this process,the electrostatic energy lost by the first capacitor is