Parallel Plate Capacitor

A Capacitor consisting of two parallel plates made of a conducting material.

• $C=\frac{q}{V}$. C = capacitance. Uses Farad as units, $1F=\frac{1C}{V}$. Most normal capacitors are in $mF,\mu F,\dots$
• ${ϵ}_0$ can be written as $\frac{F}{m}$ instead of $\frac{C^2}{N{m}^2}$, using some wacky unit conversion

$C=\frac{q}{V}=\frac{{ϵ}_{0}A}{d}$

$\Delta U=\frac{1}{2}q\Delta V$

$$U=\frac{1}{2}C{V}^2$$

$$U=\frac{q^{2}d}{2{ϵ}_{0}A}$$

$$\to U=\frac{1}{2}{ϵ}_0{E}^{2}Ad=\frac{1}{2}{ϵ}_0{E}^{2}V$$

Can be used to find electric energy density

$u=\frac{U}{V}=\frac{1}{2}{ϵ}_0{E}^2$

Capacitors are constructed from two conducting plates, with a plastic insulator between them. The sandwich is rolled up and wire leads attached to each foil.

Electrolytic Capacitor §

A flat metal area is etched to increase $A$, a vert thin insulating material of metal-oxide dieletric (to act as insulator) is grown onto the metal. Finally, a conducting paste is added to to make a very small capacitor with very high capacitance.

In a circuit of parallel capacitors, the total charge needs to be conserved (from the battery).

$q=CV$ $q_{batt}=(C_1+C_2)V$

in a series, the total potential needs to be conserved.

$V=\frac{q}{C}$