Kirchhoff's Laws

When circuits become more complex than simple series or parallel arrangements, you need a systematic method to analyse them. Kirchhoff's two laws provide exactly that. They are based on two fundamental conservation principles and together can solve any circuit problem.

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Kirchhoff's First Law (Current Law)

At any junction (node) in a circuit, the sum of the currents entering the junction equals the sum of the currents leaving the junction.

Mathematically: ΣI_in = ΣI_out

Or equivalently, if we assign positive signs to currents entering and negative signs to currents leaving: ΣI = 0

Physical Basis

Kirchhoff's first law is a statement of the conservation of charge. Charge cannot accumulate at a junction — every electron that arrives must leave. If this were not true, charge would build up at junctions, which does not happen in steady-state circuits.

Worked Example 1

At a junction, three wires meet. Wire A carries 3.0 A into the junction. Wire B carries 1.0 A into the junction. What current flows in wire C, and in which direction?