# Ohm’s Law Verified

Our second electical circuits lab was an exercise in verifying Ohm’s Law. To start, let’s look at what Ohm’s Law is and the theory behind it.

All materials have a general property of resisting the flow of electricity through themselves. This material property is quantitatively called the resistivity. (Interesting enough, resistivity is the reciprocal of conductivity.) The more difficult it is for electricity to flow through a material, the higher the resistivity value. Resistivity is purely a material property and does not depend on any particular configuration or geometry of the material. It can however be affected by temperature changes. The resistance, on the other hand, is a function of this material property, but also of the material shape. This relationship is given by:

Where R is the resistance, ρ is the resistivity, L is the length of the portion of material, and A is the uniform cross-sectional area.

The circuit element that we utilize as a model for resistance is called the resistor. The German physicist Georg Ohm investigated the relationship between the voltage across a resistor and the current through a resistor. Through this study he developed the following relationship known today as Ohm’s Law:

In order to verify this relationship for ourselves, we experimentally varied one element of the voltage, current, and resistance, kept one constant, and took readings and recorded values for the third. Then we determined the error between these recorded values and the expected values given by Ohm’s Law. Below are the tables of calculated values, measured values, and percent error for 3 different configurations.

The equipment we utilized and had set up in the first configuration consisted of a power supply (DC), a potentiometer, and the digital multimeter. The apparatus was configured as follows:

Here is the procedure for the first configuration.

1. Ensure the power supply is in the off position.
2. For part A we kept the voltage constant at 10 volts. Therefore, the first step is to connect the power supply to the digital multimeter with 2 leads, set the multimeter to read DC voltage, turn the power supply on, and adjust the voltage on the power supply until the multimeter reads 10 volts.
3. Turn the power supply back off.
4. Next connect the lead (we used red) from the positive terminal of the power supply to positive or red terminal of the potentiometer.
5. Using a lead (we used black), connect the negative or black terminal of the potentiometer to the lower left black terminal of the digital multimeter.
6. Using a lead (we used two leads in series for length and end plugs) Connect the lower right red terminal (for reading current) of the digital multimeter to the negative or black terminal of the power supply. At this point the circuit is complete.
7. Set the digital multimeter to read milliamperes of current.
8. Turn the power supply on.
9. Adjust the switches on the potentiometer to obtain the required value for the current displayed on the multimeter. (See the data tables for more. The values were 10,9,8,7… and so on.)
10. Add up and record the resistance supplied by the potentiometer that generated the corresponding current value.
11. Compare this resistance value to the resistance value predicted by Ohm’s Law. Computer the percent error for each measurement.
12. Repeat steps 9 through 11 for each required current value.

Here is a graph of our results for the first configuration. It shows the calculated values using Ohm’s Law, the measured values, and a predictive trendline with equation using the calculated values.

This first configuration gives you the idea. I have the procedure and graphs for the other implementations if anyone is interested. I have omitted them here for brevity.

Forensic Engineer, Math Nerd, Husband of @rebekahmcgehee, Father of 4, Follower of Jesus

Posted on January 31, 2011, in Electrical Engineering, Engineering and tagged , , , , , . Bookmark the permalink. 4 Comments.
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