Capacitor and Capacitance — Prelims Questions

A parallel plate capacitor has an area of $100\,\text{cm}^2$ and a plate separation of $1\,\text{mm}$. If the space between the plates is filled with a dielectric material having a dielectric constant of $5$, what is the capacitance of the capacitor? (Given: $\epsilon_0 = 8.85 \times 10^{-12},\text{F/m}$)

A capacitor has a capacitance of $20,\mu\text{F}$. If it is charged by a $100\,\text{V}$ battery, what is the magnitude of charge stored on each plate?

Which of the following changes would increase the capacitance of a parallel plate capacitor?

A capacitor is charged by a battery and then disconnected. What happens to the potential difference across its plates if a dielectric slab is then inserted between the plates?

Two parallel plate capacitors, $C_1$ and $C_2$, have the same plate area $A$. $C_1$ has a plate separation $d_1$ and $C_2$ has a plate separation $d_2$. If $d_1 = 2d_2$, what is the ratio of their capacitances $C_1/C_2$?

A capacitor has a capacitance of $10,\mu\text{F}$. If it is charged to $20\,\text{V}$, what is the energy stored in it?