Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 268

Note: We found that Ohm's law can be used for total values in a series circuit as well as for indi-
vidual parts of the circuit. Similarly, the formula for power may be used for total values:

P T = E T × I (11.29)

11.7.6.5 General Series Circuit Analysis
Now that we have discussed the pieces involved in putting together the puzzle for solving series cir-
cuit analysis, we can move on to the next step in the process: solving series circuit analysis in total.

■ EXAMPLE 11.30
Problem: Three resistors of 20 ohms, 20 ohms, and 30 ohms are connected across a battery supply
rated at 100-volt terminal voltage. Completely solve the circuit shown in Figure 11.33.

Note: To solve the circuit, the total resistance must be found first, then the circuit current can be
calculated. When the current is known, the voltage drops and power dissipations can be
calculated.

Solution: The total resistance is

R T = R 1 + R 2 + R 3

R T = 20 ohms + 20 ohms + 30 ohms = 70 ohms

By Ohm's law, the current is

E
R T

100
70

I === 143 . mps

The voltage ( E 1 ) across R 1 is

E 1 = I × R 1

E 1 = 1.43 amps × 20 ohms = 28.6 volts

The voltage ( E 2 ) across R 2 is

E 2 = I × R 2

E 2 = 1.43 amps × 20 ohms = 28.6 volts

F 1
Fuse

R 1
20 ohms

+

E
100 volts

R 2
20 ohms

-

S 1
Switch

R 3
30 ohms

FIGURE 11.33 Solving for various values in a series circuit.