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 all currents is 0

Kirchoff’s first law can also be expressed as:

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

flashcards

QuestionAnswer
What is Kirchhoff’s first law?The sum of currents entering a junction equals the sum of currents leaving the junction.
Why does Kirchhoff’s first law hold?It is due to the conservation of charge; charge cannot be created or destroyed.
How is Kirchhoff’s first law written mathematically?\sum I_{in} = \sum I_{out}
At a junction, two currents of 3A and 5A enter, and one current leaves. What is the value of the leaving current?The leaving current is 8A because 3A + 5A = 8A (sum of currents in equals sum of currents out).
What is the alternative expression of Kirchhoff’s first law?\sum I_{in} - \sum I_{out} = 0 (the sum of all currents at a junction is zero).