Mistake Master
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CED objectives

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 place

The 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.

charge does not pile up: what arrives per second leaves per second 4 A in 6 A out 2 A, and it flows IN 4 + I = 6, so I = 2 A entering. Solve it and read the sign. had the arrow been drawn outward, the answer would read −2 A: same current, same magnitude
The node equation fixes both the size and the direction. A guessed arrow that points the wrong way simply returns a negative number, which is the finished answer and not an error to repair.
correct wiring R A in line, ideal 0 Ω V across it, ideal infinite Ω swapped: both meters break the circuit A 0 Ω across R shorts it out V infinite Ω in line stops the current
Ideal resistances are what make the correct wiring invisible to the circuit: zero ohms added in series and infinite ohms added in parallel change nothing. Swapping them makes each meter maximally disruptive.

The work

3 ways in · any order
Lesson
Kirchhoff's Junction Rule

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.

Skill check · 10 scenarios
Diagnostic
10-item topic check

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.

Not started · 10 items · ~15 min
Targeted Practice
Drill a single misconception

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.

Take the diagnostic to identify your misconceptions