Electrical Calculations - Basic Mathematics for Water and Wastewater Operators - page 146

R 1
5 ohms

+

R 2
15 ohms

_

R 3
20 ohms

FIGURE 10.16 Solving for total power in a series circuit in Example 10.16.

■ Example 10.15
Problem: A series circuit consists of three resistors having values of 5 ohms, 15
ohms, and 20 ohms. Find the total power dissipation when 120 volts is applied to the
circuit (see Figure 10.16).

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 = 5 ohms + 15 ohms + 20 ohms = 40 ohms

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

E
R

120
40

T
T

I === 3amperes

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

For resistor R 1 :

P 1 = I 2 × R 1 = (3) 2 × 5 = 45 watts

For resistor R 2 :

P 2 = I 2 × R 2 = (3) 2 × 15 = 135 watts

For resistor R 3 :

P 3 = I 2 × R 3 = (3) 2 × 20 = 180 watts