Comprehensive Guide to Capacitors & Dielectrics

Capacitance

The measure of a system's ability to store electric charge per unit of potential difference.

$C$

The symbol representing capacitance in physics.

$Q$

The magnitude of charge on one of the plates of a capacitor.

$orall ext{ΔV}$

The potential difference across the plates of a capacitor.

Farad (F)

The SI unit of capacitance.

Dielectric

An insulating material inserted between the plates of a capacitor.

Dielectric Constant ($ ext{kappa}$)

The factor by which capacitance increases when a dielectric is inserted.

Electric Potential Energy

The energy stored in a capacitor due to the separation of electric charge.

Parallel Plate Capacitor

A type of capacitor consisting of two parallel conducting plates.

Gauss's Law

A law relating the electric field to the charge enclosed by a surface.

$E$

The symbol representing electric field.

Potential Difference ($ ext{ΔV}$)

The work done to move a charge from one plate to another in a capacitor.

Dielectric Constant for Vacuum

For vacuum, the dielectric constant is equal to 1.

Electric Field ($E_0$)

The external electric field produced by the capacitor plates.

Polarization

The phenomenon where molecules in a dielectric material induce a dipole moment in response to an electric field.

$u_E$

Energy density, defined as energy stored per unit volume in an electric field.

Energy Stored in Capacitor ($U_C$)

The energy stored in a capacitor, can be calculated using multiple formulas.

Energy Formula 1

U_C = rac{1}{2} rac{Q^2}{C} .

Energy Formula 2

U_C = rac{1}{2} Q V .

Energy Formula 3

U_C = rac{1}{2} C V^2 .

Electric Field inside Dielectric ($E_{net}$)

The net electric field inside a dielectric is reduced due to polarization.

Capacitors in Series

For capacitors in series, the equivalent capacitance is given by \frac{1}{C{eq}} = \sum \frac{1}{Ci}.

Capacitors in Parallel

For capacitors in parallel, the equivalent capacitance is given by C{eq} = \sum Ci.

Geometric Property of Capacitance

Capacitance is strictly a geometric property depending on the size, shape, and spacing of the conductors.

SI Unit of Capacitance

The SI unit of capacitance is Farad (F).

Air Gap in Capacitors

The insulating material between the plates in some capacitors can be air, which has a dielectric constant of approximately 1.

Farads in Microfarads

Since 1 Farad is a large capacitance, it is often expressed in microfarads (μF) or picofarads (pF).