When electrical conductors meet at a point, this point is called a junction. Just as in a closed pipe system the volume flow of an incompressible fluid must always remain constant (Hagen–Poiseuille law), the current in an electrical circuit cannot change. It follows that the sum of all incoming currents must equal the sum of all outgoing currents, keeping the junction electrically neutral. This is the formulation of the junction rule, also known as Kirchhoff’s first law, and for $n$ incoming and outgoing currents it can be written mathematically as
\[
\boxed{\sum_{k=1}^{n} I_k = 0}
\]
By convention, incoming currents are assigned positive values and outgoing currents are given negative signs.
As an example, suppose a junction in a circuit has five currents. If $I_2$ and $I_4$ are outgoing currents, while $I_1$, $I_3$, and $I_5$ are incoming currents, then the junction rule yields:
\[
-I_1 + I_2 - I_3 + I_4 - I_5 = 0
\]
Naturally, all signs can also be reversed without changing the validity of the equation.
Example problem: A junction in a circuit consists of three current-carrying wires. Two of these carry currents of 2 A and 5 A into the junction. What is the current in the third wire? Solution: $-7$ A (i.e. 7 A flowing out of the junction).