Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 281

R 2 R 3 R T = ?

R 1 2 ohms 4 ohms 8 ohms

FIGURE 11.50 Illustration for Example 11.41.

■ EXAMPLE 11.41
Problem: Find the total resistance of a 2-ohm, a 4-ohm, and an 8-ohm resistor in parallel (Figure
11.50).

Solution: Write the formula for the three resistors in parallel:

1111

=++

RRRR
T 1 2 3

Substitute the resistance values:

11
2

1
4

1
8

=++

R T

Add the fractions:

14
8

2
8

1
8

7
8

=++=

R T

Invert both sides of the equation to solve for R T :

18
7

==1.14 ohms

R T

Note: When resistances are connected in parallel, the total resistance is always less than the small-
est resistance of any single branch.

11.7.7.7 Product Over the Sum Method
When any two unequal resistors are in parallel, it is often easier to calculate the total resistance by
multiplying the two resistances and then dividing the product by the sum of the resistances:

RR
RR

×
+

1 2

R

T =

(11.38)

2 1

where R T is the total resistance in parallel, and R 1 and R 2 are the two resistors in parallel.