Find the potential difference between the points $M$ and $N$ (in $\mathrm{V}$ ) of the system shown in the figure if the emf is equal to $E=110 \mathrm{V}$ and the capacitance ratio $\frac{C_2}{C_1}$ is $2$.

Find the ratio of the magnitudes of the potential difference between the points $A$ and $B$ and that between $E$ and $F$ of the circuit shown in the figure.

Find the potential difference between the points $A$ and $B$ (in $\mathrm{V}$) in the circuit shown in the figure.

In the circuit shown, all capacitors are identical. Initially, the switch is open and the capacitor marked $C$ is the only one charged to a value $Q_0$. After the switch is closed and the equilibrium is reestablished, the charge on the capacitor marked $C_1$ is $Q$. Find the ratio of the initial change to the final charge in the capacitor $C_1$.

Find the amount by which the total energy stored in the capacitor (in $\mu \mathrm{J}$) will increase in the circuit shown in the figure after the switch $K$ is closed. Consider all capacitors are of capacitance $3 \mathrm{\mu F}$ and battery voltage is $10 \mathrm{V}$.

In the circuit shown in the figure, calculate the charge on $2 \mu \mathrm{F}$ capacitor in steady-state (in $\mu \mathrm{C}$ ).

In the circuit shown in figure, calculate the charge stored in $10 \mu \mathrm{F}$ capacitor in steady state (in $\mu \mathrm{C}$).