Capacitors & Capacitance Reference Cheat Sheet

Key Facts

• Capacitance is defined by $C = \frac{Q}{\Delta V}$, where $Q$ is charge and $\Delta V$ is potential difference.
• The SI unit of capacitance is the farad, with $1\,\mathrm{F} = 1\,\frac{\mathrm{C}}{\mathrm{V}}$.
• For a parallel-plate capacitor, $C = \kappa \epsilon_0 \frac{A}{d}$, where $A$ is plate area, $d$ is plate separation, and $\kappa$ is the dielectric constant.
• The electric field between ideal parallel plates is approximately $E = \frac{\Delta V}{d}$.
• The energy stored in a capacitor can be written as $U = \frac{1}{2}Q\Delta V = \frac{1}{2}C(\Delta V)^2 = \frac{Q^2}{2C}$.
• Capacitors in parallel have equivalent capacitance $C_{\mathrm{eq}} = C_1 + C_2 + C_3 + \cdots$ and share the same voltage.
• Capacitors in series satisfy $\frac{1}{C_{\mathrm{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \cdots$ and carry the same charge.
• Adding a dielectric increases capacitance by the factor $\kappa$, so $C = \kappa C_0$ for the same geometry.

Vocabulary

Capacitor

A device that stores separated electric charge and electric potential energy in an electric field.

Capacitance

The ratio of stored charge to potential difference, given by $C = \frac{Q}{\Delta V}$.

Dielectric

An insulating material placed between capacitor plates that increases capacitance and reduces the effective electric field.

Equivalent capacitance

The single capacitance value that can replace a network of capacitors while producing the same overall circuit behavior.

Potential difference

The voltage between two points, equal to the electric potential energy change per unit charge.

Stored energy

The energy held in a capacitor's electric field, often calculated with $U = \frac{1}{2}C(\Delta V)^2$.