KIRCHHOFF'S CURRENT LAW BASIC INFORMATION AND TUTORIALS

Kirchhoff’s current law (KCL) states that the currents entering and leaving any branch point or node in the circuit must add up to zero.

This follows directly from the conservation property: electric charge is neither created nor destroyed, nor is it “stored” (in appreciable quantity) within our wires, so that all the charge that flows into any junction must also flow out.

Thus, if three wires connect at one point, and we know the current in two of them, they determine the current in the third.

Again, the analogy of flowing water helps make this more obvious. At a point where three pipes are connected, the amount of water flowing in must equal the amount flowing out (unless there is a leak). 

For the purpose of computation, we assign positive or negative signs to currents flowing in and out of the node, respectively.

It does not matter which way we call positive, as long as we remain consistent in our definition. Then, the sum of currents into (or out of) the node is zero.

This is illustrated with the simple example in Figure 2.5, where KCL applied to the branch point proves that the current through the battery equals the sum of currents through the individual resistors.

Despite their simple and intuitive nature, the fundamental importance of Kirchhoff’s laws cannot be overemphasized. They lie at the heart of the interdependence of the different parts and branches of power systems: whenever two points are electrically connected, their voltages and the currents through them must obey KVL and KCL, whether this is operationally and economically desirable or not.

For example, managing transmission constraints in power markets is complicated by the fact that the flow on any one line cannot be changed independently of others. Thus the engineer’s response to the economist’s lamentation of how hard it is to manage power transmission: “Blame Kirchhoff.”