Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 278

Combining like terms, we obtain:

I 3 + 2 = 0

I 3 = -2 amps

Thus, I 3 has a value of 2 amps, and the negative sign shows it to be a current leaving the junction.

11.7.7.5 Parallel Circuit Resistance
Unlike series circuits, where total resistance ( R T ) is the sum of the individual resistances, in a paral-
lel circuit the total resistance is not the sum of the individual resistances. In a parallel circuit, we
can use Ohm's law to find total resistance:

E
I

R =

or

E
I

S
T

R =

T

where R T is the total resistance of all of the parallel branches across the voltage source E S , and I T is
the sum of all the branch currents.

■ EXAMPLE 11.38
Problem: Given that E S = 120 volts and I T = 26 amps, what is the total resistance of the circuit shown
in Figure 11.46?

Solution: In Figure 11.46, the line voltage is 120 volts and the total line current is 26 amps; therefore,

E
I

120
26

S
T

R === 4.62 ohms

T

Note: Notice that R T is smaller than any of the three resistances in Figure 11.46. This fact may sur-
prise you; it may seem strange that the total circuit resistance is less than that of the smallest
resistor ( R 3 , 12 ohms). If we refer back to the water analogy we have used previously, it makes
sense. Consider water pressure and water pipes, and assume that we can keep the water pres-
sure constant. A small pipe offers more resistance to the flow of water than a larger pipe, but if
we add another pipe in parallel, one of even smaller diameter, the total resistance to water flow
is decreased. In an electrical circuit, even a larger resistor in another parallel branch provides
an additional path for current flow, so the total resistance is less. Remember, if we add one
more branch to a parallel circuit, the total resistance decreases and the total current increases.

R 1 15 ohms R 2 15 ohms R 3 12 ohms

V = 120 volts

FIGURE 11.46 Illustration for Example 11.38.