Parallel Plate Capacitor — Prelims Questions

A parallel plate capacitor has a capacitance $C_0$ in air. When a dielectric slab of dielectric constant $K$ and thickness $d/2$ is introduced between the plates, completely filling half the space, what is the new capacitance?

Two parallel plate capacitors, $C_1$ and $C_2$, are connected in parallel to a battery of voltage $V$. If $C_1 = 2,mu\text{F}$ and $C_2 = 3,mu\text{F}$, what is the total charge stored by the combination?

A parallel plate capacitor is charged by a battery and then disconnected. If the plates are now pulled apart to double their separation, what happens to the potential difference across the plates?

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

A parallel plate capacitor is charged to a potential $V$ and stores energy $U$. If the capacitor is now connected to another identical uncharged capacitor in parallel, what is the total energy stored in the system?

Which of the following statements is TRUE regarding the force between the plates of a charged parallel plate capacitor?