Kirchhoff's Loop Rule
▶︎ Watch it animatedinteractive step-through · ~3 min · optional ⚙︎ Open the appletLoop Rule Walk · pick a loop and a direction, commit a sign to every term, and watch whether the potential staircase closesThe loop rule states that the potential changes around any closed path in a circuit sum to zero, which is energy conservation for a charge that returns to its starting point. Each change is priced by the direction of travel: a resistor crossed along the current is a drop and crossed against it a rise, and a battery walked from negative to positive is a rise and the other way a drop. The rule applies to source-free loops as well, and applying it to two parallel branches is where their shared potential difference comes from. Drawn as a graph of potential against position, it requires flat wires, steps of size $IR$, and a return to the starting value.
Three errors dominate. Assigning signs by component type, so every source is a plus and every resistor a minus, which breaks the moment a second battery faces the other way or a guessed current points backward. Writing loop equations only for paths that contain a source, which leaves too few equations for the unknowns and misses that parallel branches share a potential difference. And sketching the potential around a loop so that it does not return to its starting value, usually by putting drops along ideal wires or sizing a resistor step wrongly.
The work
3 ways in · any order
Lesson
Kirchhoff's Loop Rule
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Prices every loop-rule crossing by the direction of the walk rather than by component type, applies the rule to source-free loops, and uses the closure of the potential graph as an audit.
Diagnostic
10-item topic check
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Ten items spanning the failure modes of this topic: giving every battery a plus and every resistor a minus, writing equations only for loops containing a source, and sketching a potential graph that does not return to its starting value. Take it cold to find which one is yours, or after the lesson to confirm it is not.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.