Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 279

I T = 26 A

120 volts

R T = 4.26 ohms

FIGURE 11.47

Circuit equivalent to that of Figure 11.46.

A

R 1 = 10 ohms

R 2 = 10 ohms

FIGURE 11.48 Two equal resistors connected in parallel.

Back to Example 11.38 and Figure 11.46. What we essentially demonstrated in working this par-
ticular problem is that the total load connected to the 120-V line is the same as the single equivalent
resistance of 4.62 ohms connected across the line. It is probably more accurate to call this total resis-
tance the equivalent resistance , but by convention R T (total resistance) is generally used, although
they are often used interchangeably. The equivalent resistance is illustrated in the equivalent circuit
shown in Figure 11.47. Other methods are used to determine the equivalent resistance of parallel
circuits. The most appropriate method for a particular circuit depends on the number and value of the
resistors; for example, consider the parallel circuit shown in Figure 11.48. For this circuit, the follow-
ing simple equation is used:

R
N

R

eq =

(11.36)

where
R eq = Equivalent parallel resistance.
R = Ohmic value of one resistor.
N = Number of resistors.

Thus,

10 ohms

R eq = = 5 ohms

2

Note: Equation 11.36 is valid for any number of equal value parallel resistors.

Key Point: When two equal value resistors are connected in parallel, they present a total resistance
equivalent to a single resistor of one half the value of either of the original resistors.

■ EXAMPLE 11.39
Problem: Five 50-ohm resistors are connected in parallel. What is the equivalent circuit resistance?

Solution: Using Equation 11.36:

R
N

50
5

R

eq ===

10 ohms