In a parallel circuit the electricity has alternative paths to follow (see Figure 26.2) and consequently the total resistance of the circuit is not equal to the sum of the individual resistances. The total amperage in the circuit is determined by the total resistance, but total resistance is determined differently from series circuits. The amperage through any path is determined by the voltage at the path and the resistance of the path.

The total resistance can be determined by more than one method. In one method, the inverse of the total resistance is the sum of the inverses of each resistance in

FIGURE 26.2. Parallel circuit.

FIGURE 26.2. Parallel circuit.

the parallel circuit:

This equation requires solving for a common denominator or reducing the fractions to a decimal. The easiest way to determine a common denominator is to multiply the denominators. When this method is used for the circuit in Figure 26.2, the total resistance is:

30.8

1 0.9625

Using this method, the total resistance of the circuit is 0.96 Q.

When reducing the fractions to a decimal, it is important to remember that the result is the inverse.

Problem: Determine the total resistance of the parallel circuit in Figure 26.2 by reducing the fractions.

Solution:

0.9625

Compare the total resistance of this circuit to the total resistance of the series circuit. With the same resistors, the total resistance is much less in a parallel circuit.

Another method is to solve for the equivalent resistance of pairs of resistors, until all of the resistance is reduced to a single resistance. This is accomplished by using the equation:

R1 x R2

When the circuit has more than two resistors, determine the equivalent resistance (Re) for any two, and then combine it with the third, and so on, until only one resistance remains. The resistance of the circuit in Figure 26.2 with this method is:

Using this method the total resistance is 1.0 Q, which agrees with the other two methods.

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