Kirchhoff's Junction Rule
▶︎ Watch it animatedinteractive step-through · ~3 min · optional ⚙︎ Open the appletJunction Lab · label the branch currents before solving, get a negative back, then wire a meter in the wrong placeThe junction rule is charge conservation at a point: the currents entering a node equal the currents leaving it, instant by instant. Combined with the loop rule it closes any DC network, provided the equations are counted correctly: $N$ nodes give $N - 1$ independent junction equations, and the remaining unknowns are supplied by independent loops. Every unknown current is assigned a guessed direction first, and the algebra is written against those arrows.
Two errors dominate. Treating a negative solved current as a mistake, then either restarting with reversed arrows or flipping one sign inside an otherwise unchanged system, which corrupts equations that still appear solvable. A negative value already IS the answer: the magnitude is right and the true direction is opposite the arrow. And wiring meters backward: an ammeter belongs in series and is ideally zero resistance, a voltmeter belongs in parallel and is ideally infinite resistance. Clipped across an element the ammeter short-circuits it, and inserted in a branch the voltmeter opens it, so in both cases the reading describes a circuit that no longer exists.
The work
3 ways in · any order
Lesson
Kirchhoff's Junction Rule
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Balances current at a node, establishes that a negative solved current is the finished answer, counts the junction and loop equations a network needs, and fixes ammeter and voltmeter placement along with the loading errors real meters introduce.
Diagnostic
10-item topic check
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Ten items spanning the failure modes of this topic: mis-signing a node balance, restarting a solution because a current came out negative, flipping one sign inside an otherwise unchanged system, clipping an ammeter across an element, inserting a voltmeter in line, and misreading what a loaded meter is telling you. 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.