# In this lesson you will learn what a voltage divider is, how to calculate the resistance to get a specific voltage, and how they relate to potentiometers.

In the last lesson you wired your potentiometer to your meter.  Fully counterclockwise was 0VDC and fully clockwise was 24VDC.  However most analog voltages are 0-10VDC, not 0-24VDC.  We need to lower the voltage on the outside of our potentiometer from 24VDC to 10VDC.  To do this, we will add a 7K ohm resistor in in series with the potentiometer as show in the image to the right.

Why a 7K resistor to make 10 VDC?  The short and simple answer is if you take your source voltage times the resistance of your potentiometer divided the voltage that you need across the potentiometer minus the resistance of your potentiometer will equal the value of the resistor you need to put in series with your potentiometer.  That was a mouthful so let's look at the equation.

• Vs = Voltage Source
• Vd = Voltage desired across the potentiometer
• Rp = Potentiometer resistance
• Rt = Total circuit resistance needed

Vs * Rp / Vd = Rt

Plugging in the numbers of our circuit:

24 VDC * 5,000 ohm / 10 VDC = 12,000 ohms of total resistance needed.

We already have 5,000 ohms of resistance through the potentiometer so we can subtract that and get the value of resistance needed to get 10VDC.

12,000 ohms - 5,000 ohms = 7,000 ohms or 7 kilo-ohms or a 7K resistor.

How does a Voltage Divider circuit work?  Using this Ohm’s law pie chart from this lesson we can determine the current that is going to go through this circuit by taking our voltage and dividing it by the resistance.

I = Amps

E = Voltage

R = Resistance

I = E/ R

24 VDC / 12,0000 amps = 0.002 amps.

This 0.002 amps will flow through every part of our circuit so using that and the resistance of the potentiometer, so based off of our Ohm's Law Power Formulas and Pie Chart we can determine the voltage across the resistor using the formula E (Voltage) = I (Amps) * R (Resistance):

E = I * R

E = Voltage

I = Amps

R = Resistance

0.002 Amps * 5,000 ohms = 10 VDC

What happened to the other 14 volts?

The other didn't "burn up".  Plugging in the 7K resistor into the formula above:

0.002 Amps * 7,000 ohms = 14 VDC

24 VDC source = 14VDC across the 7K resistor + 10VDC across the 5K potentiometer.  The voltage was evenly divided among the resistance points of the circuit hence the term Voltage Divider.

## Next Steps

Go to the Analog Circuits Training Lesson Series to select your next lesson.  There are also many other Lesson Series on PLC Programming and Industrial Automation.