Refer to Figure 12-97 for an example. Point A and point B represent two junctions or nodes in the circuit with three resistive branches in between. The voltage source provides a total current IT into node A. At this point, the current must divide, flowing out of node A into each of the branches according to the resistive value of each branch. Kirchhoff’s Current Law states that the current going in must equal that going out. Following the current through the three branches and back into node B, the total current IT entering node B and leaving node B is the same as that which entered node

Figure 12-98 shows that the individual branch currents are:

The total current flow into the node A equals the sum of the

The total current entering node B is also the same.

Figure 12-99 illustrates how to determine an unknown current in one branch. Note that the total current into a junction of the three branches is known. Two of the branch currents are known. By rearranging the general formula, the current in branch two can be determined.

It can now be easily seen that the parallel circuit is a current divider. As shown in Figure 12-96, there is a current through each of the two resistors. Because the same voltage is applied across both resistors in parallel, the branch currents are inversely proportional to the ohmic values of the resistors. Branches with higher resistance have less current than those with lower resistance. For example, if the resistive value of R2 is twice as high as that of R1, the current in R2 is half of that of R1. All of this can be determined with Ohm’s Law.

By Ohm’s Law, the current through any one of the branches can be written as:

The voltage source appears across each of the parallel resistors and RX represents any one the resistors. The source voltage is equal to the total current times the total parallel resistance.

And

This formula is the general current divider formula. The current through any branch equals the total parallel resistance divided by the individual branch resistance, multiplied by the total current.

Most of the circuits that the technician encounters will not be a simple series or parallel circuit. Circuits are usually a combination of both, known as series-parallel circuits, which are groups consisting of resistors in parallel and in series. An example of this type of circuit can be seen in Figure 12-100. While the series-parallel circuit can initially appear to be complex, the same rules that have been used for the series and parallel circuits can be applied to these circuits. The voltage source provides a current out to resistor R1, then to the group of resistors R2 and R3 and then to the next resistor R4 before returning to the voltage source. The first step in the simplification process is to isolate the group R2 and R3 and recognize that they are a parallel network that can be reduced to an equivalent resistor. Using the formula for parallel resistance,