Kirchoff's Node Law

Two different examples are given below. Notice that the value and direction of the current is given through battery A as well as through resistors B and F. The goal of the two examples is to determine the directions of the current through battery D and battery E.

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. Battery E 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 resistor B is directed into the node. The current through resistor F is directed away from the node. We will make a random guess that the current through battery E is away from 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

I_B = I_E + I_F

where I_B, I_E and I_F represent the currents through B, E and F respectively. Substituting in values gives:

2A = I_E + 1A.

Solving for IE gives I_E = +1A. The positive sign indicates that our guess above was correct. Hence, the current through battery E really is directed away from the node which means that it is directed downward through battery E.