Random Physics - Electrostatics And Current Electricity Practice

**Case Study: Capacitance and Dielectrics** A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges $Q$ and $-Q$ with a potential difference $V = V_1 - V_2$ between them. The ratio $\frac{Q}{V}$ is a constant, denoted by $C$, 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 them. When a parallel plate capacitor is charged, the electric field $E_0$ is localised between the plates and is uniform throughout. When a slab of a dielectric is inserted between the charged plates (having charge density $\sigma$), the dielectric is polarised by the field. Consequently, opposite charges appear on the faces of the slab near the plates, with a surface charge density of magnitude $\sigma_p$. For a linear dielectric, $\sigma_p$ is proportional to $E_0$. 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.