The distance between plates of a parallel plate capacitor is $d$. Another thick metal plate of thickness $\frac{d}{2}$ and area same as that of the plates is so placed between the plates, that it does not touch the plates. The capacity of the resultant capacitor

The capacity and the energy stored in a parallel plate condenser with air between its plates are, respectively, $C_0$ and $W_0$. If the air between the plates is replaced by the glass (dielectric constant$=5$). Find the capacitance of the condenser and the energy stored in it.

A capacitor of capacitance $10 \mu \mathrm{F}$ is connected to battery of emf $20 \mathrm{V}$. Without disconnecting the source a dielectric ($K=4$) is introduced to fill the space between the two plates of the capacitor. Calculate the charge before the dielectric was introduced.

A capacitor of capacitance $10 \mu \mathrm{F}$ is connected to battery of emf $20 \mathrm{V}$. Without disconnecting the source a dielectric ($K=4$) is introduced to fill the space between the two plates of the capacitor. Calculate the charge after the dielectric is introduced.

Find the equivalent capacitance of the combination of capacitors between the points $A$ and $B$ as shown in the figure. Also, calculate the total charge that flows in the circuit when a $100 \mathrm{V}$ battery is connected between the points $A$ and $B$.

Three capacitors each of capacitance $9 \mathrm{pF}$ are connected in series. What is the total capacitance of the combination?

The following figure shows the initial charges on the capacitors. After the switch $S$ is closed, find the charge on the capacitor $C_1$.

The following figure shows the initial charges on the capacitors. After the switch $S$ is closed, find the work done by the battery.