Multiple choiceQuestion 1 · Recall
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By the end you can state Kirchhoff's first law, explain why it follows from conservation of charge, and use it to find an unknown current at a junction.
Stand at a junction: a point in a circuit where two or more wires meet.
Charge carriers arrive along some of those wires and leave along others. In a steady circuit they cannot simply stop at the junction and stay there, because that would mean charge collecting in one place.
So charge must arrive as fast as it leaves. The rate at which charge flows is the current, so the total current into the junction equals the total current out.
Picture a water pipe that splits into two. Whatever volume of water flows into the split each second has to flow out of the branches each second, because the water has nowhere else to go.
The analogy is reliable for the "what goes in must come out" idea. It stops being accurate in one way: a wire is not a pipe that gradually fills with charge. The junction rule is about a circuit in a steady state, not about a container filling up.
Kirchhoff's first law
The sum of the currents entering a junction is equal to the sum of the currents leaving it.
Conservation of charge says charge is never created and never destroyed.
Now watch one junction for one second. Suppose 3.0 C of charge arrives and only 2.0 C leaves. Where did the other 1.0 C go? There is nowhere for it to go: it cannot vanish, and it cannot stay at the junction without charge building up there.
So the charge arriving per second equals the charge leaving per second. Divide both by one second, and you have the junction rule: current in equals current out.
Worked example: Finding the unknown current
At a junction, 2.0 A arrives along one wire and 1.2 A arrives along another. One wire leaves carrying 0.80 A. What current leaves along the fourth wire?