This fundamental law results from the conservation of charge. It applies to a junction or node in a circuit -- a point in the circuit where charge has several possible paths to travel.
In Figure 1, we see that IA is the only current flowing into the node. However, there are three paths for current to leave the node, and these current are represented by IB, IC, and ID.
Once charge has entered into the node, it has no place to go except to leave (this is known as conservation of charge). The total charge flowing into a node must be the same as the the total charge flowing
out of the node. So,
IB + IC + ID = IA
Bringing everything to the left side of the above equation, we get
(IB + IC + ID) - IA = 0
Note:
The convention we have chosen here: current flowing into the node are taken to be negative, and currents flowing out of
the node are positive. It should not really matter which you choose to be the positive or negative current, as long as you stay
consistent. However, it may be a good idea to find out the convention used in your class.