Define electric capacity- Derive an expression the capacitance of a parallel plate capacitor in which a dielectric medium of dielectric constant K fills the space between the plates- Draw the necessary diagram-

Question

Toppr Admin · Accepted Answer

Capacitance or electric capacity indicates the ability of a system to store charge. It is defined as the ratio of charge stored in the conductors to the potential difference across the conductors. Its SI unit is Farad ( $F$ ). Hence:
$C = \frac{Q}{V}$

To derive the expression of capacitance of parallel plate capacitor of conductor area $A$ and distance between the conductors as $d$ with a dielectric of dielectric constant $K$ carrying a charge $Q$ and potential difference $V$ , refer to the attached figure.
Electric field between plates of the capacitor can be found using Gauss Law.
$E = \frac{σ}{K ε_{o}}$
$E = \frac{Q}{K ε_{o} A}$ as $σ = \frac{Q}{A}$

Electric field is defined as the gradient of potential.
$E = \frac{V}{d}$
$⟹ V = \frac{Q d}{K ε_{o} A}$

By definition of capacitance,
$C = \frac{Q}{V}$
$= \frac{K ε_{o} A}{d}$

Define electric capacity. Derive an expression for the capacitance of a parallel plate capacitor in which a dielectric medium of dielectric constant K fills the space between the plates. Draw the necessary diagram.

Define electric capacity. Derive an expression for the capacitance of a parallel plate capacitor in which a dielectric medium of dielectric constant $K$ fills the space between the plates. Draw the necessary diagram.