# Kirchhoff's Current Law

## Intro

Kirchhoff's first law states that the amount of current flowing into a point is the same as the amount flowing out:

This law is also known as *Kirchhoff's current law*, *Kirchhoff's point rule*, or *Kirchhoff's junction rule*. Sometimes this is also called the *conservation of charge*; current cannot be lost here because it has nowhere to go. This might seem like common sense, given what we know about the physics of electricity, but at the time he discovered this (1845), very little was actually known about the underlying physics.

### Branching Circuits

When circuits branch off at a node, they're known as *branching circuits*. Consider the following parallel branching circuit:

Using Kirchhoff's current law, in conjunction with Ohm's law, we can determine the total amount of current flowing through the circuit. First, let's calculate the amount of current flowing through each resistor (circuits `A -> D`

and `B -> C`

):

`Given:`

I = V / R

Therefore:

I (at Resistor A-D) = 12V / 10Ω = 1.2A

I (at Resistor B-C) = 12V / 1.5Ω = 8A

Given Kirchhoff's current law which states the sum of currents entering a junction is equal to the sum of the currents leaving a junction, we can determine that the current entering junction `A`

is equal to the amount of current flowing from `A -> D`

plus `B -> C`

:

`Current at Junction A = 1.2A + 8A = 9.2A`

Additionally, the current flowing in and out of `D`

is also `9.2A`

.