Capacitance

$C\equiv \frac{Q}{V}$

• The capacitance between two charges on separate conductors
• $V$ is the voltage

$Q=CV,C=\frac{Q}{V},V=\frac{Q}{C}$

• 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.

$U_C=\frac{1}{2}C{V}^2=\frac{1}{2}QV=\frac{Q^2}{2C}$

$C_{\text{plates}}=\kappa {\epsilon }_0\frac{A}{d}$

• $\kappa$ is the dielectric constant
• ${\epsilon }_0$ is the permittivity of free space
• $A$ is the area of a single plate
• $d$ is the distance between the plates

$C_{\text{plate}}={\epsilon }_0=\frac{A}{d}$

• Check this later

$C_{\text{series}}={\left(\sum _{i=0}^N\frac{1}{C_i}\right)}^{-1}$

$C_{\text{parallel}}=\sum _{i=0}^N{C}_i$