Kirchoff's first law

The sum of currents entering a ‘junction’ is equal to the sum of currents leaving the junction.

This is due to the conservation of charge - charge cannot be created or destroyed.

We can write this as:

\sum I_{in} = \sum I_{out}

Example

At a junction, three currents meet. Two of the currents are entering the junction with values of 3A and 5A. The third current is leaving the junction. What is the value of the third current?

• Sum of currents entering the junction: 3A + 5A = 8A
• So the current leaving the junction must also be 8A due to Kirchoff’s first law.

Sum of all currents is 0

Kirchoff’s first law can also be expressed as:

\sum I_{in} - \sum I_{out} = 0