Kirchoff's Node Law

Two different examples are given below. Notice that the directions of the current are given through resistors B, C, D and E. The goal of the two examples is to determine the directions of the current through battery A and resistor G.

Example #1

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. Resistor G is colored red to remind you that you are trying to determine the direction of 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 resistors B, D and E are all directed into the node. Resistor G is the only other resistor that is connected to the node. Hence, Kirchoff’s Loop Law implies that the current through G must be directed away from the node. In other words, the current through battery G is directed downward.

Example #2

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 direction of the current though it.