Ohm’s Law
By John Boehringer and David Bezinque. The production of this lab was funded in part by a grant from the McKinney Education Foundation, Spring 2006.
Ohm’s Law is one of the most frequently used laws in the analysis of the electrical circuits. For resistors that are “Ohmic,” that is, they follow Ohm’s Law, there is a relationship between the electric potential difference V across that resistor and the current I passing through that resistor. This is true as long as the temperature remains constant. That relationship is
V = IR ,
where the resistance R of the resistor is a constant that is independent of V and I and is measured in Ohms. Some resistors do not follow Ohm’s Law. These are called “non-Ohmic” resistors and have a variable resistance that depends on the current passing through them. The filament of many common light bulbs is a non-Ohmic resistor. However, despite these properties, in a static situation, even the resistance of a non-Ohmic resistor follows the proportion established by Ohm’s Law. That is
This relationship holds true for any resistor as long as the current and voltage in the circuit remain constant.
Problem
- Devise a method to determine the current through a single resistor series circuit for all possible potential differences.
- Become familiar with Ammeters and Voltmeters (as digital current and voltage probes, respectively).
- Verify Ohm’s Law for a resistor of known resistance.
Materials
Windows PC w/ LoggerPro software1 high wattage resistor (R>10 Ohms)
Current ProbeVoltage Probe
Banana adapter wiresAlligator Clips
3 D-Cell batteries (1.5 V each) or a variable voltage power supply
Preliminary Questions
- When using sensors and/or meters to analyze electric circuits, voltmeters are ALWAYS connected in parallel with the component across which you are observing a potential difference (voltage). Usually this means attaching the leads of the voltmeter on opposite sides of a resistor. Why can’t the leads of a voltmeter be connected in series with a resistor?
- In the space below sketch a graph of voltage (V) versus current (I) for an Ohmic resistor. In a different color sketch, on the same axes, a possible graph of V versus I for a non-Ohmic resistor. Show your instructor.
Procedure
1. DO NOT SAVE ANYTHING on the PC!
2. Connect current probe on Ch. 2 and voltage probe on Ch. 1 on the LabPro and attach to the USB port on PC. Be sure to plug in your LabPro to the electrical outlet using the AC adapter!
3. Prepare computer for data collection by starting Logger Pro software. Allow your PC to automatically detect the LabPro and the sensors. If the PC does not apprea to recognize the probes, ask your laboratory instructor for assistance.
4. Although you can set up your own experimental file, in the Physics with Computers folder you will find a experimental file entitled Ohm’s Law (Exp 25). It is suggested that you utilize this file as it should already contain software defaults that can make your procedure easier. In some cases where older voltage probes are being used, a window will appear indicating that the computer cannot detect the probes that the file is calibrated for. If this occurs, ask your instructor for assistance.
5. It will be necessary to calibrate or zero your probes. This file already provides you an option to do this. Be certain that the probe is not hooked up to any circuit elements. Hold the sensor steady and wait for the readings in the bottom left to stabilize. Look to the right Collect button. Click the button that says “Zero.” This will zero your probes. The voltage probe should not require calibration as it measures a potential difference between the two leads.
6. Set up the circuit below. The COLORS of the insulation on your wires are unimportant. These colors are for reference in larger circuits. Since we are not using a physical switch apparatus, you will use a disconnected wire as a switch. Do NOT connect all leads (i.e., complete the circuit) until your instructor has verified your set-up. If you have your circuit constructed incorrectly, you run the risk of damaging your sensors.
Be sure that you connect the voltmeter in parallel with the resistor and the ammeter in series with the resistor.
7. Once your instructor has verified your experimental set-up, take a look at your data window. Your PC has been pre-programmed to take individual data points on command, rather than a continuous, time-graph. Your graph window should display current (I) in Amps on the horizontal axis, and Voltage (V) in volts on the vertical axis. If this is not what you see, left click on the title on each axis and select the correct option. When you click Collect (Do NOT do it now!) the software will begin to sample both your current reading and voltage measurement at that moment in time. When the reading is stable (it will experience minute fluctuations due to the high sensitivity of the sensors) you will click Keep. The second time you click Keep a second data pair will be recorded. Ultimately, this experiment will yield four (4) data points, from which a best fit regression can be extracted and analyzed. If you have a variable power supply (voltage source) you can take more data points by simply increasing the voltage in steady intervals and collecting data at each step.
8. With the circuit OFF (no batteries in place), but all of your probes connected, click Collect once. Now click Keep. The PC should have recorded a point of zero (0) current and zero (0) voltage or possibly some very small values close to zero due to solid state fluctuations in the electronics. If you should “keep” a data point that you do not want, you can delete it by right clicking on the point. If you have difficulty, ask your instructor for assistance.
9. Add one (1) D-cell battery to the circuit or turn on your variable voltage source to a low voltage (between 1 and 2 volts). Connect the circuit so that current is allowed to flow through the resistor. Click Keep to record data. Disconnect the circuit.
10. Now connect the circuit with two (2) batteries in place (approx. 3 volts total) as shown below.
When your switch is in the closed position and current is moving, click Keep to record data. Disconnect the circuit.
11. Now connect the circuit with three (3) batteries in place (approx. 4.5 volts total). Connect the circuit and click Keep to collect your final data point. Disconnect the circuit. Click Stop.
12. Record your data in the table below.
Resistor Stated Value: ______ ______ (Tolerance)
Data Point / Voltage (V) / Current (A)1
2
3
4
Drawing Conclusions
1. What is the shape of your voltage (y) vs. current (x) graph? Based on your premises from the beginning of the lab, identify your resistor as Ohmic or non-Ohmic.
2. We need to verify Ohm’s Law for this resistor. Click on the function fit button (f(x)= ) in the toolbar at the top of your screen. Since your data is highly linear, select the function of the form y=mx+b to be fit to the data. Click Try Fit. Click OK and exit the curve fit window. The linear function and its equation should appear on your graph. Write the function below. If you do this on your calculator or in Excel, be careful that you match the correct variables with the correct axes on your graph.
3. Refer to procedure step number 8. Why was your first data set zero for both current and voltage? Since we are verifying Ohm’s Law for the resistor you are working with, does this value make sense? Explain.
4. Now look at your y-intercept value from your best-fit function. Is the y-intercept zero or very close?
5. Now look at the slope of your best-fit line. How does this number compare with the value, in Ohms, stamped on your resistor? Do a percent difference calculation ([|exp-stated|/stated] x 100)and if there is significant divergence in these values and explain why this error occurred.
6. Now, based on your conclusions, re-write the equation from number 2 (above) in terms of the variables V, I, and R. It may be helpful to recall which variables were represented on your vertical and horizontal axes.
Extending
1. Describe how you could use your data to predict the current through your resistor if 50 V were applied to this circuit (assuming your wires didn’t melt).
2. Voltmeters and Ammeters are specially designed to work in parallel and series with a resistor, respectively. One of these devices has a very large resistance (in theory, we assume it to be infinite) and one has a very low resistance (again, in theory, we assume it to be zero). Which device, voltmeter or ammeter, has infinite resistance? Zero resistance? Explain your reasoning.
3. Assuming you had a good voltage source of known output, say, a 6 V lantern battery. Develop a similar technique to the one you used in the lab today to find the resistance of three identical resistors of unknown resistance. (hint: there are many solutions to this problem)