Hello 2098489,

# Voltage divider

The governing equation in your application is the voltage divider rule:

V_{Out} = V_{in}\dfrac{R_2}{R_1 + R_2}

You have selected 1.5 kΩ for R1 and 100 Ω for R2. With a presumed Arduino running using the default rail (5 VDC) as the voltage reference for the Analog To Digital Converter (ADC):

5 = V_{in}\dfrac{100}{100 + 1500}

Solving for V_{in} yields approximately 80 VDC. Your calculations are reasonable but could be improved as we will explore later in this note.

# Power Dissipation

We can use Ohm’s Law to determine the power dissipation.

R_{total} =R_1 + R_2 = 1500 + 100 = 1600\ \Omega

Current = \dfrac{Voltage}{Resistance} = \dfrac{80}{1600} = 0.05\ A

Power = Current \ x \ Voltage = 0.05 * 80 = 4 \ W

Consequently, you will be able to use 1/4 W resistors. Through-hole resistors of this size are reasonably easy to work with. However, you may want to use 1/2 W resistors as they are slightly larger and easier to read.

This is unnecessarily high dissipation. Let’s shift all values up by a factor of 10 and recalculate.

R_{total} =R_1 + R_2 = 15000 + 1000 = 16,000\ \Omega

Current = \dfrac{Voltage}{Resistance} = \dfrac{80}{16,000} = 0.005\ A

Power = Current \ x \ Voltage = 0.005 * 80 = 0.4 \ W

This is an improvement but still higher than necessary. I’ll leave it to you to select a better resistor pair. Know that the maximum recommend value for R2 is approximately 10 kΩ. However, to be safe, perhaps 5 kΩ is a better value.

# Improvements

Chances are, you will be unhappy with the results as the voltage will be off and the resolution (smallest measured voltage increment) will be larger than desired. There are three things you can do to improve this situation:

1. Shift the Arduino to an internal voltage reference. Instead of using the voltage rail you should use one of the internal references such as analogReference(INTERNAL1V1). By comparison the internal reference is more stable and doesn’t drift as the Arduino is loaded down. It also eliminates the uncertainty associated with your PC’s USB port. Note that you will need to adjust your voltage divider accordingly.

2. Optimally select your resistors as I outlined in this article. The trick is to determine the ratio of R1 and R2. You then find the closest resistor pair. For your application, recommend selecting the input voltage as 10% higher than the highest anticipated voltage e.g, 50 * 1.10 and the output voltage as the ADC reference e.g., 1.1.

3. Use low tolerance resistors sush as 1%. They will cost a bit more, but the values will be closer improving your chance of correctly measuring the voltage. Alternatives include hand selecting resistors from the batch or providing a calibration value for the Arduino.

Be safe as you have crossed into the world of high voltage with the very real potential to hurt of kill you or someone you love. Here defined as anything above approximately 30 volts.

Recommend you find a mentor to guide you in this exciting endeavor.

Best Wishes,

APDahlen

Ref:

Voltage Divider Conversion Calculator | DigiKey

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