Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 280

+

10 A

R 1 = 3 ohms R 2 = 10 ohms

-

5 A

15 A

FIGURE 11.49 Illustration for Example 11.40.

What about parallel circuits containing resistance of unequal value? How is equivalent resistance
determined? Example 11.40 demonstrates how this is accomplished.

■ EXAMPLE 11.40
Problem: Refer to Figure 11.49.

Solution:
Given:
R 1 = 3 ohms
R 2 = 10 ohms
E a = 30 volts

We know that
I 1 = 10 amps
I 2 = 5 amps
I t = 15 amps

and can now determine R eq :

E
I

30
15

a
t

R === 2 ohms

eq

Key Point: In Example 11.40, the equivalent resistance of 2 ohms is less than the value of either
branch resistor. Remember, in parallel circuits the equivalent resistance will always be smaller than
the resistance of any branch.

11.7.7.6 Reciprocal Method
When circuits are encountered in which resistors of unequal value are connected in parallel, the
equivalent resistance may be computed by using the reciprocal method .
Note: A reciprocal is an inverted fraction; the reciprocal of the fraction 3/4, for example, is 4/3.
We consider a whole number to be a fraction with 1 as the denominator, so the reciprocal of
a whole number is that number divided into 1; for example, the reciprocal of R T is 1/ R T .
The equivalent resistance in parallel is given by the following formula:

1111 1

=++++ (11.37)

RRRR R

T 1 2 3 n

where R T is the total resistance in parallel, and R 1 , R 2 , R 3 , and R n are the branch resistances.