Circuit Analysis (Kirchhoff's Laws) Cheat Sheet

Key Facts

• Kirchhoff's current law states that the sum of currents entering a junction equals the sum of currents leaving it, so $\sum I_{\text{in}} = \sum I_{\text{out}}$.
• Kirchhoff's voltage law states that the algebraic sum of voltage changes around any closed loop is zero, so $\sum \Delta V = 0$.
• Ohm's law connects voltage, current, and resistance using $V = IR$.
• For a resistor, moving in the direction of conventional current gives a voltage drop of $\Delta V = -IR$.
• For a resistor, moving opposite the direction of conventional current gives a voltage rise of $\Delta V = +IR$.
• Moving through a battery from the negative terminal to the positive terminal gives a voltage rise of $+\varepsilon$.
• Moving through a battery from the positive terminal to the negative terminal gives a voltage drop of $-\varepsilon$.
• Electric power can be calculated using $P = IV$, $P = I^2R$, or $P = \frac{V^2}{R}$.

Vocabulary

Junction

A junction is a point in a circuit where three or more conducting paths meet.

Loop

A loop is any closed path in a circuit that starts and ends at the same point.

Conventional current

Conventional current is the direction positive charge would move, from higher electric potential to lower electric potential through a resistor.

Voltage drop

A voltage drop is a decrease in electric potential, often written as $\Delta V = -IR$ across a resistor in the direction of current.

Electromotive force

Electromotive force, or emf, is the energy supplied per unit charge by a source such as a battery, represented by $\varepsilon$.

Algebraic sum

An algebraic sum includes positive and negative signs, so voltage rises and voltage drops must be added with their correct signs.