Capacitor Networks Worked Examples Cheat Sheet

Key Facts

• For capacitors in parallel, the equivalent capacitance is $C_{\text{eq}} = C_1 + C_2 + C_3 + \cdots$.
• For capacitors in series, the equivalent capacitance satisfies $\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \cdots$.
• The charge on a capacitor is related to voltage by $Q = CV$.
• Capacitors in parallel have the same voltage, so $V_1 = V_2 = V_3 = V_{\text{battery}}$.
• Capacitors in series have the same charge, so $Q_1 = Q_2 = Q_3 = Q_{\text{series}}$.
• The total energy stored in a capacitor can be found using $U = \frac{1}{2}CV^2$, $U = \frac{Q^2}{2C}$, or $U = \frac{1}{2}QV$.
• In a mixed network, first reduce obvious series or parallel groups, find $C_{\text{eq}}$, then expand the circuit backward to find individual $Q$ and $V$ values.

Vocabulary

Capacitance

Capacitance is the ability of a device to store charge per unit voltage, measured in farads using $C = \frac{Q}{V}$.

Equivalent capacitance

Equivalent capacitance is the single capacitance value that would store the same total charge at the same voltage as the whole network.

Series connection

A series connection is an arrangement where capacitors are connected end to end so each capacitor stores the same charge.

Parallel connection

A parallel connection is an arrangement where capacitors share the same two nodes, so each capacitor has the same voltage.

Stored energy

Stored energy is the electric potential energy held in a charged capacitor, often calculated with $U = \frac{1}{2}CV^2$.

Node

A node is a point in a circuit where connected wires are at the same electric potential.