Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 276

I 1 I 2

I T I 3

1 A

100 volts 2 A R 1 2 A R 2 R 3

FIGURE 11.42 Illustration for Example 11.34.

Solution: The formula for total current is

I T = I 1 = I 2 = I 3

Thus,

I T = 2 + 2 + 1 = 5 amps

The total current, then, is 5 amps.

■ EXAMPLE 11.35
Problem: Two branches, R 1 and R 2 , across a 100-V power line draw a total line current of 20 amps
(Figure 11.43). Branch R 1 takes 10 amps. What is the current ( I 2 ) in branch R 2 ?
Solution: Beginning with Equation 11.33, transpose to find I 2 and then substitute given values:

I T = I 1 + I 2

I 2 = I T - I 1

I 2 = 20 - 10 = 10 amps

The current in branch R 2 , then, is 10 amps.

■ EXAMPLE 11.36
Problem: A parallel circuit consists of two 15-ohm and one 12-ohm resistors across a 120-V line
(see Figure 11.44). What current will flow in each branch of the circuit and what is the total current
drawn by all the resistors?

Solution: There is 120-V potential across each resistor. Using Equation 11.34, apply Ohm's law to
each resistor:

V
R

120
15

V
R

120
15

V
R 3

120
12

I == = 8amps, I = == 8amps, I = = 10 amps

1 2 3

1 2

I 1 = 10 A

I T = 20 A I 2 = ?

100 volts

R 1 R 2

FIGURE 11.43 Illustration for Example 11.35.