Two different examples are given below. The five black arrows represent the directions of the current through resistors A, C, D and G as well as through battery B. The goal of the two examples is to determine the values of the current through resistor E and battery F.
Kirchoff's Node Law states that the sum of the currents into a node equals the sum of the currents out of the node. A node is a location where two or more wires are connected together. The circuit at right is identical to the one above except that the circuit elements that are connected to one particular node have been highlighted. The flashing dot is the node. All but one of the circuit elements that are connected to the flashing node are colored green. Battery F is colored red to remind you that you are trying to determine the current through it.
To apply Kirchoff’s Node Law, you must separate the currents that are directed into the node from those that are directed away from it. For the circuit above, the current through resistor D is directed into the node. The current through resistor G is directed away from the node. We will make a random guess that the current through battery F is into the node. This guess is purely random. We could just as easily have guessed the opposite. The analysis below will tell us whether the guess is correct or incorrect. Kirchoff’s Node Law gives:
Total Current Into Node = Total Current Out of Node
ID + IF = IG
where ID, IF and IG represent the currents through D, F and G respectively.
Substituting in the values shown in the circuit diagram gives:
3A + IF = 2A.
Solving for IF gives IF = -1A. The negative sign indicates that our guess above was in fact incorrect. In reality, the current through battery F is directed away from the node which means that it is directed upward through battery F.
The circuit at right is identical to the circuit in the previous example, except that the circuit elements attached to a different node are highlighted. As before, most of the circuit elements are colored green. The red resistor is colored differently to remind you that you are trying to determine the current though it.
Total Current Directed Toward Node = Total Current Directed Away From Node
IC + IG = IE
2A + 2A = IE.
Notice that resistors A and C are connected in series. A common misconception is that the 2A current through resistor A should be added to the 2A current through resistor C to give the current into the node. There are not two different 2A currents, however, so they should never be added. The charges that flow through resistor A will subsequently flow through resistor C. They are the same charges, not two different sets of them. There is never a reason to add the currents through resistors that are connected in series.