Electronics/KCL

Kirchoff's Current Law
Current is conserved.

Current flowing into a junction is equal to that flowing out.

I1 = I2 + I3


 * $$ I_{1} = I_2 + I_3 + \cdots + I_n \,\! $$

Current is the flow of electrons through a piece of metal. Given the sheer number of electrons involved it is similar to the flow of water through a pipe. When the pipe branches the water has multiple paths to travel. The only rule is that the amount of water entering any place has to be equal to the amount of water leaving any that place. Otherwise the pipe would explode from the pressure or the water would cease to exist.

Here is more about Kirchhoff's laws which can be integrated here