# What is capacitance?

Jun 2, 2014

Capacitance is a measure of how much charge a capacitor can hold at a given voltage.

A capacitor is a device which can store electrical charge. A simple capacitor can be formed with two parallel plates of conducting material separated by air, plastic, or some other non-conducting material. When the plates have opposite electric charge, these charges can be held in place on the plates for long periods of time. In this simple model, consider what would happen if you doubled the area of the plates. This would double the amount a charge which the plates could hold.

Decreasing the distance between the plates will increase the electric field in the space between. This also increases the capacitance.

The simple equation for a Parallel Plate Capacitor is:
$C = \setminus \kappa \cdot {\epsilon}_{0} \cdot \frac{A}{d}$

where $d$ is the distance between the plates, $A$ is the surface area of each plate. The $\setminus \kappa$ is a constant (called the dielectric constant) which relates to the dielectric properties of the material between the two plates and ${\epsilon}_{0}$ is permittivity of "free space". Since ${\epsilon}_{0}$ is constant, one can just think of this equation as a constant times an area divided by a distance.

Capacitors in circuits play an electrical role analogous to springs in mechanical systems. Springs store mechanical energy when stretched; the further they are stretched the greater the force they apply. Capacitors store electrical energy when they are charged, and the more charge they hold, the greater the voltage across them.

The following analogies hold:
$\setminus \textrm{\mathrm{di} s \tan c e s t r e t c h e d} \setminus \leftrightarrow \setminus \textrm{c h a r \ge o n p l a t e s}$
$\setminus \textrm{s p r \in g f \mathmr{and} c e} \setminus \leftrightarrow \setminus \textrm{v o < a \ge}$
$\setminus \textrm{s p r \in g c o n s \tan t} \left(k\right) \setminus \leftrightarrow \setminus \textrm{o \ne o v e r \cap a c i \tan c e} \left(\frac{1}{C}\right)$
Whereas a high $k$ spring is very stiff, a high $C$ capacitor is very electrically ''squishy.'' Capacitance is the electrical squishyness. The same way the shocks in your car can smooth out the impact of bumps in the road, capacitors can smooth out temporal variations in voltage.