A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges Q and -Q with potential difference…

A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges Q and -Q with potential difference $\displaystyle \mathrm{V}=\mathrm{V}_{1}-\mathrm{V}_{2}$ between them. The ratio $\displaystyle \frac{\mathrm{Q}}{\mathrm{V}}$ is a constant, denoted by $\displaystyle \mathrm{C}$ and is called the capacitance of the capacitor. It is independent of Q or V. It depends only on the geometrical configuration (shape, size, separation) of the two conductors and the medium separating the conductors. When a parallel plate capacitor is charged, the electric field $\displaystyle \mathrm{E}_{0}$ is localised between the plates and is uniform throughout. When a slab of a dielectric is inserted between the charged plates (charge density $\displaystyle \sigma$ ) , the dielectric is polarised by the field. Consequently opposite charges appear on the faces of the slab, near the plates, with surface charge density of magnitude $\displaystyle \sigma_{\mathrm{p}}$. For a linear dielectric $\displaystyle \sigma_{\mathrm{p}}$ is proportional to $\displaystyle \mathrm{E}_{0}$. Introduction of a dielectric changes the electric field, and hence, the capacitance of a capacitor, and hence, the energy stored in the capacitor. Like resistors, capacitors can also be arranged in series or in parallel or in a combination of series and parallel.

Consider a capacitor of capacitance C, with plate area A and plate separation d, filled with air[Fig. (a) ]. The distance between the plates is increased to $\displaystyle 2$ d and one of the plates is shifted as shown in Fig. (b) . The capacitance of the new system now is: