Capacitance
#Physics
$\displaystyle C\equiv \frac{Q}{V}$
- The capacitance between two charges on separate conductors
- $\displaystyle V$ is the voltage
$Q=CV,\space C=\frac{Q}{V},\space V=\frac{Q}{C}$
- Units of capacitance $C$ are $\text{Farad }(\frac{C}{V})$
- The capacitance is dependent only on the geometry of the capacitor, and not the voltage or charge held.
$U_C=\frac{1}{2}CV^2=\frac{1}{2}QV=\frac{Q^2}{2C}$
$C_\text{plates}=\kappa\varepsilon_0\frac{A}{d}$
- $\kappa$ is the dielectric constant
- $\displaystyle {\varepsilon}_{0}$ is the permittivity of free space
- $A$ is the area of a single plate
- $d$ is the distance between the plates
$C_\text{plate}=\varepsilon_0=\frac{A}{d}$
- Check this later