Environmental Engineering Reference
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I T = 20 A
I 1 = 10 A
I 2 = ?
R 1
R 2
100 V
FIGURE 10.23
Illustration for Example 10.19.
I T
I 1
I 2
I 3
120 V
R 1
15 ohms
R 2
15 ohms R 3
12 ohms
FIGURE 10.24
Illustration for Example 10.20.
I T = I 1 + I 2
I 2 = I T - I 1 = 20 amperes - 10 amperes = 10 amperes
The current in branch R 2 , then, is 10 amperes.
Example 10.20
Problem: A parallel circuit consists of two 15-ohm and one 12-ohm resistors across
a 120-volt line (see Figure 10.24). What current will flow in each branch of the circuit
and what is the total current drawn by all the resistors?
Solution: There is a 120-volt potential across each resistor. Using Equation 10.13,
apply Ohm's law to each resistor:
V
R
120
15
I
== =
8
amperes
1
1
V
R
120
15
I
== =
8
amperes
2
2
V
R
120
12
I
== =
10
amperes
3
3
p arallel C irCuit r esistanCe
Unlike series circuits, where total resistance ( R T ) is the sum of the individual resis-
tances, in a parallel circuit the total resistance is not the sum of the individual resis-
tances. In a parallel circuit, we can use Ohm's law to find total resistance:
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