3 The Voltage Divider
voltage. The voltage has thus been divided between the two resistors. The idea can be extended to circuits with more than two resistors and with different values.
A voltage divider consists of two or more resistors connected in series with a voltage source. Voltage dividers are used to obtain a smaller voltage from a larger source voltage. As you saw in 2 Series Circuits, the voltage drops in a series circuit equal the source voltage. If you have two equal resistors in series, the voltage across each will be one-half of the source
Consider the series circuit illustrated in Figure 3-7.
Figure 3-7
is larger than the other? Since both resistors must have the same current, Ohm's Law tells us that the larger resistor must drop a larger voltage. In fact, the voltage across any resistor in a series circuit can be found by finding the fraction of the resistor in question to the total resistance, and multiplying by the source voltage. For example, if a series resistor represents one-third of the total resistance, the voltage across it will be one-third of the source voltage.
This equation is a general form of the voltage divider equation. It can be stated as: "The output voltage from a voltage divider is equal to the input voltage multiplied by the ratio of the resistance between the output terminals to the total resistance." When several resistors are used, the output is generally taken with respect to the circuit common for the
Figure 3-8
(a)
(b)
Figure 3-9
Voltage dividers can be made to obtain variable voltages by using a potentiometer. The full range of the input voltage can be made available at the output as illustrated in Figure 3-9(a). If one desires to limit the range of the output voltage, this can be done by using fixed resistors in series as illustrated in Figure 3-9(b).
Resistor
The Voltage Divider

R1
R2
R3
R4
RT
10.0 V
Construct the circuit you designed and measure the actual output voltage. Indicate the measured value on your drawing above.
Use two of the resistors from this experiment to design a divider with a +10 V input and a +7.5 V output. Draw your design in the space provided below.
Construct the circuit you designed and measure the actual output voltage. Indicate the measured value on your drawing above.
the range of voltages. Assume V s is + 10 V. Use the voltage divider formula to
compute the minimum and maximum voltages available from this circuit:
Vmin =
Vmax =

voltages:
just the power supply to 4.0 V and measure the current. Record the current in Table 2-4. Continue taking current readings for each of the voltages listed in Table 2-4.
Vmin =
Vmax =

The voltage divider formula can be extended to find the voltage in a series circuit between any number of resistors. Call the resistance that is between the output terminals 𝑅𝑥. Then the voltage across this resistance can be written:
If the resistors are equal, the voltage across 𝑅2 will be one-half the source voltage. But what happens if one of the resistors
divider as shown in Figure 3-8. In this case the output voltage can be found by substituting the value of 𝑅2 and 𝑅3 for 𝑅𝑥 as shown.
To find the voltage across 𝑅2, the ratio of 𝑅2 to 𝑅𝑇 is multiplied by the source voltage. That is:
10 kΩ

𝑉𝑥 (measured)
Using a 1.8 kΩ, a 8.2 kΩ, and a 10 kΩ resistor, design a voltage divider with a +5.0 V output from a source voltage of +10 V. Draw your design in the space provided below.
The circuit shown in Figure 3-9 (b) uses a 10 kΩ potentiometer and 𝑅1 and 𝑅2 to limit the range of voltages. Assume 𝑉𝑆 is +10 V. Use the voltage divider formula to compute the minimum and maximum voltages available from this circuit:
8.2 kΩ
4.7 kΩ
2.7 kΩ
Figure 3-11
Figure 3-10
Connect the series circuit shown in Figure 3-11.
Observe the voltages measured in step 5. In the space provided below, draw a voltage divider showing how you could obtain an output of +7.1 V.
Construct the circuit analysed in step 11. Measure the minimum and maximum output voltages:
Table 3-9
Measure each resistor listed in Table 3-9 and record the measured value. Compute the total resistance for a series connection by adding the listed values and entering the computed value in Table 3-9.

Connect the resistors in series as illustrated in Figure 3-10. Measure the total resistance of the series connection and verify that it agrees with your computed value. Enter your measured value in Table 3-9.
Apply the voltage divider rule to each resistor, one at a time, to compute the expected voltage across that resistor. Use the measured values of resistance and a source voltage of +10 V. Record the computed voltages (𝑉𝑥) in Table 3-9, column 4.
Turn on the power and measure the voltage across each resistor. Record the measured voltage drops in Table 3-9, column 5. Your measured voltages should agree with your computed values.