# Kirchhoff's Current and Voltage Laws

From Mech

## Contents |

## Kirchhoff's Current Law

Kirchhoff's Current Law says that the current going into a junction is equal to the current going out of a junction. In other words, the sum of the currents entering the node must be zero (if we consider currents leaving the node to be a negative current entering the node). Consider the following diagram:

File:Kirchhoffs current law node diagram.jpg

For the node **A** in the center, *i1* and *i2* are entering the node, and *i3* and *i4* are leaving the node. We would write:

which can also be written as

Note that *i7* is equal to *i2*; we can prove this by analyzing node **B**. We can also treat everything between node **C** and **D** as one big node, and conclude that *i5* is equal to *i6* without having to know the value of any of the currents within.