Capacitance — Prelims Questions

Three capacitors of capacitances $2,\mu\text{F}$, $3,\mu\text{F}$, and $6,\mu\text{F}$ are connected in series. The equivalent capacitance of the combination is:

A parallel plate capacitor has capacitance $C_0$ in air. When a dielectric slab of dielectric constant $K$ and thickness $d/2$ is introduced in the space between its plates (total separation $d$), the new capacitance becomes:

A $10,\mu\text{F}$ capacitor is charged to $100\,\text{V}$. The energy stored in the capacitor is:

A parallel plate capacitor is charged by a battery and then disconnected. A dielectric slab is then inserted between the plates. Which of the following quantities remains unchanged?

Two capacitors $C_1$ and $C_2$ are charged to $V_1$ and $V_2$ respectively. When they are connected in parallel, the common potential is:

A parallel plate capacitor has a capacitance of $50\,\text{pF}$. If the area of the plates is $25\,\text{cm}^2$ and the separation between them is $1\,\text{mm}$, what is the dielectric constant of the material between the plates? (Given $\epsilon_0 = 8.85 \times 10^{-12},\text{F/m}$)