Electrical Calculations - Basic Mathematics for Water and Wastewater Operators - page 152

I T I 1 I 2 I 3

100 V 2 A R 1 2 A R 2 1 A R 3

FIGURE 10.22 Illustration for Example 10.18.

By Ohm's law, each branch current equals the applied voltage divided by the
resistance between the two points where the voltage is applied. Hence, for each
branch we have the following equations:

E
R

V
R

1
1

Branch 1: I ==

1

1

E
R

V
R

2
2

Branch 2: I == (10.14)

2

2

E
R

V
R

3
3

Bra nch3: I ==

3

3

With the same applied voltage, any branch that has less resistance allows more cur-
rent through it than a branch with higher resistance.

■ Example 10.18
Problem: Two resistors, each drawing 2 amperes, and a third resistor that draws 1
ampere are connected in parallel across a 100-volt line (see Figure 10.22). What is
the total current?

Solution: The formula for total current is

I T = I 1 + I 2 + I 3

Thus,

I T = 2 amperes + 2 amperes + 1 amperes = 5 amperes

The total current, then, is 5 amperes.

■ Example 10.19
Problem: Two branches, R 1 and R 2 , across a 100-volt power line draw a total line
current of 20 amperes (Figure 10.23). Branch R 1 takes 10 amperes. What is the cur-
rent ( I 2 ) in branch R 2 ?
Solution: Beginning with Equation 10.13, transpose to find I 2 and then substitute
given values: