Kirchhoff's Current Law
Current into a node equals current out.
Formula
Variables
Example
If 3 A and 2 A flow into a junction, exactly 5 A must flow out.
How it works
Kirchhoff's Current Law says that at any junction in a circuit, charge does not pile up, so the total current entering the node must equal the total current leaving it. This follows from conservation of electric charge: if more current entered than left, charge would accumulate at the node, which does not happen in steady circuit analysis. The law applies to each node regardless of the number of connected branches.
When to use it
Use this law whenever you need to find unknown branch currents in circuit networks, especially at junctions with multiple paths. It is a standard tool in nodal analysis and in checking whether a proposed current split in a circuit is physically consistent.
Worked example, step by step
At a junction, two currents enter: 4.5 A and 1.2 A. Using Kirchhoff's Current Law: sum of currents in = sum of currents out 4.5 A + 1.2 A = I_out,total 5.7 A = I_out,total So the total current leaving the junction must be 5.7 A. If one outgoing branch carries 3.0 A, the other outgoing branch must carry 5.7 A - 3.0 A = 2.7 A.
Common mistakes to avoid
- Forgetting to include every branch connected to the node
- Mixing up current directions and using the wrong sign for in/out currents
- Applying the law to a whole circuit instead of to a single junction/node
Did You Know?
Kirchhoff's current law is simply conservation of charge — what flows into a junction must flow out.
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