Series vs Parallel Circuits Cheat Sheet

Key Facts

• Ohm’s law relates voltage, current, and resistance using $V = IR$.
• In a series circuit, the equivalent resistance is $R_{\text{eq}} = R_1 + R_2 + R_3 + \cdots$.
• In a series circuit, the current is the same through every component, so $I_{\text{total}} = I_1 = I_2 = I_3$.
• In a series circuit, the battery voltage is shared by the components, so $V_{\text{total}} = V_1 + V_2 + V_3 + \cdots$.
• In a parallel circuit, the equivalent resistance is found with $\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots$.
• In a parallel circuit, the voltage across each branch is the same, so $V_{\text{total}} = V_1 = V_2 = V_3$.
• In a parallel circuit, total current is the sum of branch currents, so $I_{\text{total}} = I_1 + I_2 + I_3 + \cdots$.
• Bulb brightness is proportional to power, and power can be calculated with $P = IV$, $P = I^2R$, or $P = \frac{V^2}{R}$.

Vocabulary

Series circuit

A circuit with only one path for current, so every component has the same current.

Parallel circuit

A circuit with two or more branches, so current can split and travel through different paths.

Equivalent resistance

The single resistance value that would have the same effect as all resistors in the circuit combined.

Current

The rate of flow of electric charge, measured in amperes, and represented by $I$.

Voltage

The electric potential difference that pushes charge through a circuit, measured in volts, and represented by $V$.

Power

The rate at which electrical energy is transferred or used, measured in watts, and represented by $P$.