Electrical Calculations - Basic Mathematics for Water and Wastewater Operators - page 144

is equal to the sum of the two individual resistances, or 12 ohms. Using Ohm's law,
the circuit current may be calculated as follows:

E
R

30
12

T
T

I === 2.amperes

Because we know that the value of the resistors is 6 ohms each, and the current
through the resistors is 2.5 amperes, we can calculate the voltage drops across the
resistors. The voltage ( E 1 ) across R 1 is, therefore,

E 1 = I × R 1 = 2.5 amperes × 6 ohms = 15 volts

Because R 2 is the same ohmic value as R 1 and carries the same current, the voltage
drop across R 2 is also equal to 15 volts. Adding these two 15-volt drops together gives
a total drop of 30 volts, exactly equal to the applied voltage. For a series circuit then,

E T = E 1 + E 2 + E 3 + … + E n (10.9)

where
E T = Total voltage (V).
E 1 = Voltage across resistance R 1 (V).
E 2 = Voltage across resistance R 2 (V).
E 3 = Voltage across resistance R 3 (V).

■ Example 10.14
Problem: A series circuit consists of three resistors having values of 10 ohms, 20
ohms, and 40 ohms. Find the applied voltage if the current through the 20-ohm
resistor is 2.5 amp.

Solution: To solve this problem, first draw a circuit diagram and label it as shown in
Figure 10.15.

R 1
10 ohms

+

R 2
20 ohms

E = ?

-

40 ohms 2.5 amps

R 3

FIGURE 10.15 Solving for applied voltage in a series circuit in Example 10.14.