A slab of copper of thickness $\frac{d}{2}$ is introduced between the plates of a parallel plate capacitor which touches one of the plates of the capacitor, where $d$ is the separation between its two plates. If the capacitance of the capacitor without copper slab is $C$ and with copper slab is $C^{\text{'}}$, then $\frac{C^{\text{'}}}{C}$ is

Two parallel plates of the same metal and same area are placed between the plates of a parallel plate capacitor of capacity $C$, If the thickness of each plate is equal to $\frac{1}{5}\mathrm{th}$ of the distance between the plates of the original capacitor then the capacity of the new capacitor is :-

A network of four capacitors of capacity equal to $C_1=C, C_2=2C, C_3=3C \text{and} C_4=4C$ are connected to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is :—

A 10 volts battery is connected to three capacitors; $C_1=2 \mathrm{\mu F}, C_2=3 \mathrm{\mu F} \text{and} C_3=5 \mathrm{\mu F},$ as shown. The charges on the capacitors $C_1, C_2 \text{and} C_3$ are respectively :

Two materials of dielectric constants $k_1 \text{and} k_2$ are introduced to fill the space between the two parallel plates of a capacitor as shown in figure. The capacity of the capacitor is :

Two capacitors, $3 \mathrm{\mu F}$ and $4 \mathrm{\mu F}$, are individually charged across a $6 \mathrm{V}$ battery. After being disconnected from the battery, they are connected together with the negative plate of one connected to the positive plate of the other. What is the final total energy stored ?

In an isolated parallel plate capacitor of capacitance $C$, the four surfaces have charges $Q_1, Q_2, Q_3 \text{and} Q_4$ as shown. The potential difference between the plates is :