Electric and Magnetic Fields: Capacitors

Capacitance

A capacitor is a device that stores electrical energy in an electric field.
The capacitance of a capacitor is the charge stored per unit potential difference.
Capacitance is measured in farads (F) which is equivalent to coulombs per volt (C/V).
The formula for capacitance is C = Q/V, where C is capacitance, Q is charge, and V is voltage.

Capacitor Construction

A capacitor is commonly made from two conductive plates separated by an insulator, known as the dielectric.
The larger the surface area of the plates and the closer they are together, the greater the capacitance.
The type of dielectric material used also affects the capacitance.

Energy Stored in a Capacitor

The energy stored in a capacitor is given by the formula W = 0.5CV^2, where W is the energy, C is the capacitance, and V is the voltage across the capacitor.
Alternatively, energy can also be calculated using the formula W = 0.5QV, where Q is the charge on the capacitor.
The energy is stored in the electric field between the plates.

Charging and Discharging

As a capacitor charges, current decreases and the potential difference across the capacitor increases.
A graph of potential difference (V) against charge (Q) for a capacitor will be a straight line through the origin.
The area under this graph is equivalent to the work done or energy stored in the capacitor.
When discharging, the current and voltage decrease exponentially over time.
The equations for discharging over time are Q = Q0e^(-t/RC) for charge and V = V0e^(-t/RC) for voltages, where Q0 and V0 are initial charge and voltage respectively, R is resistance, C is capacitance, and t is time.
The time constant (τ) for a circuit containing a resistor and capacitor is given by τ = RC.
This time constant represents the time taken for the quantity (charge, current or voltage) to fall to 1/e (approximately 37%) of its initial value.