Kirchoff's current law
Kirchoff's Current Law (KCL) is a law of electrical engineering which states that the sum of all currents flowing into any point on a circuit is zero. Since a current of I0 flowing into a point is equal to a current of -I0 flowing out of that point, this is equivalent to saying that the sum of all currents flowing into a point is equal to the sum of all currents flowing out of that point.
This can be derived from the Law of Conservation of Electric Charge. Since a current is defined as moving charge, when a current flows into a point on a circuit, that point experiences a buildup of charge. Since charge does not build up in a circuit (else the current would stop flowing), the charge must go somewhere - in other words, a current must flow out of that point. No charge stays at that point, so the current flowing out must be equal to the current flowing in.
- See also: Kirchoff's voltage law