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Voltage Dividers
A series circuit acts as a voltage divider. You will learn what this term means and why
voltage dividers are an important application of series circuits. After completing this
section, you should be able to:
Use a series circuit as a voltage divider
Apply the voltage-divider formula
Use the potentiometer as an adjustable voltage divider
Describe some voltage-divider applications
To illustrate how a series string of resistors acts as a voltage divider, we will examine
Figure 16, where there are two resistors in series. As you already know, there are two
voltage drops: one across R1 and one across R2. We call these voltage drops V1 and
V2, respectively, as indicated in the diagram.
FIGURE 16 Two-resistor voltage divider.
+
I
R1
V1
-
Vs
+
R2
V2
-
Since the same current flows through each resistor, the voltage drops are proportional
to the resistance values. For example, if the value of R2 is twice that of R1, then the
value of V2 is twice that of V1. In other words, the total voltage drop divides among
the series resistors in amounts directly proportional to the resistance values.
For example, in Figure 16, if VS is 10 V, R1 is 50 , and R2 is 100 , then V1 is onethird the total voltage, or 3.33 V, because R1 is one-third the total resistance. Likewise, V2 is two-thirds VS, or 6.67 V.
Voltage-Divider Formula
With a few calculations, a formula for determining how the voltages divide among
series resistors can be developed.
I = V1 also I = V2 and I = VS where RT = R1 + R2
R1
R2
RT
 V2 = VS from which V2 = VS x R2 and V1 = VS x R1 This only applies if R2 is
not
R2 RT
R1+R2
R1+R2
loaded.
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Current-Divider Formula for Two Branches
The reason for doing so is that two parallel resistors are often found in practical
circuits. We start by restating the formula for the total resistance of two parallel
branches.
RT = R1R2 also V = I1R1, V = I2R2 and V = ITRT
R1 + R2
Figure 17
IT
I1
Vs
R1
I2
I1R1= ITRT
I1 =
R1R2 x IT
(R1+ R2)x R1
I1 =
R2 x IT
(R1+ R2)
R2
Also
I2R2= ITRT
I2 =
R1R2 x IT
(R1+ R2)x R2
I2 =
R1 x IT
(R1+ R2)
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