$A$ $2 \mu F$ capacitor is charged to a potential $V_1 = 10 \ V$. Another $4 \mu F$ capacitor is charged to a potential $V_2 = 20 \ V$. The two capacitors are then connected in a single loop,with the positive plate of one connected to the negative plate of the other. What heat is evolved in the circuit? (in $\mu J$)

$A$ capacitor $C_{1}$ of capacitance $5\,\mu F$ is charged to a potential of $30\,V$ using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor $C_{2}$ of capacitance $10\,\mu F$ as shown in the figure. When the switch is closed,charge flows between the capacitors. At equilibrium,the charge on the capacitor $C_{2}$ is . . . . . . $\mu C$.

$A$ $20\,\mu F$ capacitor is charged to a potential of $500\,V$ and then connected in parallel to a $10\,\mu F$ capacitor charged to $200\,V$. What is the common potential in $V$?

$A$ $20 \mu F$ capacitor is charged to $5 V$ and isolated. It is then connected in parallel with an uncharged $30 \mu F$ capacitor. The decrease in the energy of the system will be (in $\text{J}$)

$A$ $3\ \mu F$ capacitor is charged to a potential of $300\ V$ and a $2\ \mu F$ capacitor is charged to $200\ V$. They are then connected in parallel with plates of opposite polarity joined together. What is the amount of charge (in $\mu C$) that flows through the connecting wires?

Two capacitors $C_1$ and $C_2$ are charged to $120 \ V$ and $200 \ V$ respectively. It is found that connecting them together the potential on each one can be made zero. Then