Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 267

Solution:
Given:
R 1 = 5 ohms
R 2 = 15 ohms
R 3 = 20 ohms
E = 120 volts

The total resistance is found first:

R T = R 1 + R 2 + R 3

R T = 5 + 15 + 20 = 40 ohms

Using total resistance and the applied voltage, we can calculate the circuit current:

E
R

120
40

T
T

I === 3amps

Using the power formula, we can calculate the individual power dissipations:

For resistor R 1 :

P 1 = I 2 × R 1

P 1 = (3) 2 × 5 = 45 watts

For resistor R 2 :

P 2 = I 2 × R 2

P 2 = (3) 2 × 15 = 135 watts

For resistor R 3 :

P 3 = I 2 × R 3

P 3 = (3) 2 × 20 = 180 watts

To obtain total power:

P T = P 1 + P 2 + P 3

P T = 45 + 135 + 180 = 360 watts

To check our answer, the total power delivered by the source can be calculated:

P = E × I

P = 120 volts × 3 amps = 360 watts

Thus, the total power is equal to the sum of the individual power dissipations.