Capacitor and Capacitance Revision Notes

Vocabulary flashcards covering core electrostatics concepts including conductors, insulators, capacitance, parallel plate capacitors, dielectric constants, and electric polarisation.

Conductors

Materials through which electric charge can flow easily, with most metals serving as primary examples.

Insulators (Dielectrics)

Non-conducting substances through which electric charge cannot flow (e.g., glass, rubber, wood) because they possess no or a negligible number of free charges or charge carriers.

Bound Charges

Positively charged ions and fixed electrons that remain held in their fixed positions within a conductor after free electrons leave their parent atoms.

Capacitor

A device used to store electrostatic potential energy or charge, comprising two conductors separated by an insulating medium.

Capacitance of a Conductor

The constant of proportionality $C$ between the charge $q$ given to an isolated conductor and the resulting increase in its electrical potential $V$, defined by $q = C V$.

Farad ($\text{F}$)

The SI unit of electrical capacitance, defined as one Coulomb per Volt ($1\,\text{F} = 1\,\text{C}\,\text{V}^{-1}$).

Dimensions of Capacitance

The dimensional formula for capacitance, expressed as $[\text{M}^{-1}\,\text{L}^{-2}\,\text{T}^{4}\,\text{A}^{2}]$.

Capacitance of an Isolated Spherical Conductor

The capacitance of an isolated spherical conductor of radius $a$, given by $C = 4\pi\varepsilon_0 a$, which is directly proportional to its radius.

Parallel Plate Capacitor

The most common capacitor design, consisting of two parallel conducting plates separated by a dielectric medium or an air gap.

Capacitance of an Air-Filled Parallel Plate Capacitor

The capacitance of a parallel plate capacitor in the absence of a dielectric medium, given by $C_0 = \frac{\varepsilon_0 A}{d}$, where $A$ is the plate area and $d$ is the plate separation.

Capacitance of a Partially Filled Capacitor

The capacitance of a parallel plate capacitor containing a dielectric slab of thickness $t$ and dielectric constant $K$, given by $C = \frac{\varepsilon_0 A}{d - t + \frac{t}{K}}$.

Capacitance of a Fully Filled Capacitor

The capacitance when a dielectric of constant $K$ completely fills the space between the plates ($t = d$), given by $C = \frac{K \varepsilon_0 A}{d} = K C_0$.

Capacitance with a Metal Slab

The capacitance of a parallel plate capacitor when a conducting metal slab ($K = \infty$) of thickness $t$ is introduced between the plates, given by $C = \frac{\varepsilon_0 A}{d - t}$.

Dielectric Constant ($K$)

The ratio of the capacitance of a capacitor with a dielectric medium between its plates to its capacitance with vacuum between the plates ($K = \frac{C_{\text{medium}}}{C_{\text{vacuum}}}$), also known as relative permittivity ($\varepsilon_r$).

Electric Polarisation

The phenomenon in which the net electric field inside a dielectric is reduced to $E_0 - E_p$ due to an opposing induced field $E_p$ when placed in an external field $E_0$, satisfying $K = \frac{E_0}{E_0 - E_p}$.