Two different examples are given below. Notice that the values of the currents through resistors A, C, E and battery F are given. The goal of the two examples is to determine the values of the currents through resistors B and G.
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. The flashing dot is a node. The circuit elements that are connected to this node have been highlighted. The resistor that is colored green has a current with a known value. Resistor B is colored red to remind you that you are trying to determine the value of the current through it.
Since there are only two circuit elements attached to the node, one must have a current directed into the node and the other a current directed out of the node. According to Kirchoff’s Node Law, these currents must be equal. The current through resistor A is 4A. Hence the current through resistor B is the same.
Notice that resistors A and B are connected together in series. The currents through resistors that are connected in series are always equal.
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, the battery that is colored green has a current with a known value. The red resistor has a current value that is unknown.
Note that resistor G and battery F are connected in series. An application of Kirchoff’s Node Law shows that the currents through resistors that are connected together in series are always equal.