Kirchhoff's loop rule

The rule is one line, $\sum \Delta V = 0$ around any closed loop, and its justification is conservation of energy: a charge carried once around a loop returns to its starting point, so the electric potential energy it gained and lost has to cancel exactly.

Fix a sign convention before writing anything, then keep it for the whole loop. Pick a direction to walk. With that direction chosen:

• Crossing a source from its negative terminal to its positive terminal counts as $+\mathcal{E}$; the other way counts as $-\mathcal{E}$.
• Crossing a resistor in the same direction as the current in it counts as $-IR$; against the current it counts as $+IR$.

Walk the whole loop, add the terms, set the sum to zero. Both the walking direction and the current directions you guessed at the start are arbitrary. A current that comes out negative simply flows the other way, and nothing needs redrawing.

Neither Kirchhoff rule is printed on the AP Physics 2 equation sheet, so this one is known rather than looked up. The CED also expects you to read a graph of electric potential against position around a loop: it steps up at the battery, falls across each resistor, and finishes at the value it started from.

The junction rule is its companion, and actually reducing a network is the job of the series and parallel guide.