Ohm's Law and the Measurement of Resistance I. INTRODUCTION An electric current flows through a conductor when a potential difference is placed across its ends. The potential difference is generally in direct proportion to the current. The constant of proportionality is called the resistance. The mathematical representation of this relation is called Ohm's law and it is written as V = IR (1) where V is the potential difference in volts, I is the current in amperes, and R is the resistance measured in ohms (Ω). Resistance, as the name implies, is a measure of how difficult it is for the electrons to flow through a conductor. If a steady current is flowing through a material with a high resistance, it will require a lot of work (provided by the potential difference) to move the electrons through. If the resistance is small, only a little work will be required to move the electrons through and the voltage will be small. All conductors, for the most part, satisfy Ohm's law. Some materials like semiconductors and superconductors don't follow this law and are said to be non-ohmic. The resistance of a conductor depends on many things. The longer the conductor the more work will be required to move electrons through, and hence a greater resistance. If the conductor has a small cross section, there is less space for the electrons to flow and hence more resistance. Usually, there is also a dependence on the temperature of the substance. And finally, some materials are intrinsically better conductors than others. For example, silver is a better conductor than gold. The measure of a material s ability to conduct electrons is called the conductivity σ. A more common and useful measurement is the resistivity ρ of a material. The resistivity is simply the inverse of the conductivity, ρ = 1/σ (2) A conductor made of a material of resistivity ρ, length l, and uniform cross sectional area A, has a resistance R given by R = ρl/a (3) 1
In this experiment you will measure resistance and you will find the resistance of a conductor by measuring the current through the conductor at various voltages. The slope of the graph of voltage versus current will be the resistance. Figure 1. The connections for the voltmeter and ammeter. II. APPARATUS You will need the following items for this experiment: Variable power supply Two digital multimeters (used as a voltmeter and an ammeter) Two unknown resistors Wire for connections Light bulb 2
A voltmeter should only be connected in parallel, across the leads of a device as shown in Figure 1. The voltage reading will be the voltage drop in the device. An ammeter is always connected in series into the circuit as shown in Figure 1. The ammeter can be damaged by connecting it in parallel. Schematically, our circuit is the simple loop shown in Figure 2 -- a power supply connected in series to a resistor. (The resistor will be different items, but in each case it is the object that we are studying.): Figure 2. A single loop circuit For the power supply we will use a variable power supply (represented by the symbol for a battery-- two parallel lines of different lengths). This easily allows us to vary the potential difference. Next we will add the two meters. It would be a good idea to begin color coding your circuits. In a short while it will be critical to know which wires are connected to the negative terminal (lower potential) and which are connected to the higher side. Typically we use black wires to indicate the lower potential side of the circuit and red to indicate the higher potential. Connect up the two multimeters, one to read the current through the resistor (notice that the current is the same through all parts of our simple circuit as it is not created or destroyed) and another to read the potential drop across the resistor. Remember that the ammeter (current measuring device) needs to be in series with the compenent you re investigating, that way the current travels through the meter. The voltmeter needs to be in parallel with the component under investigation. 3
Figure 3. Measuring both current and voltage III. PROCEDURE A. Unknown Resistors To see Ohm's law at work, you will measure combinations of voltage and current for two unknown resistances and measure the slope of the graphs. 1. Set up the equipment as described above. The power should be off when making connections. 2. The power supply should be set for 0 volts. The multimeter should be on the 2 VDC range. (This means it will read values up to 2V.) The ammeter should be connected for the 50 ma range. 3. Turn on the power. By slowly turning the dial on the power supply, you can adjust the voltage across the resistor. As you do this the current should also change. Make ten measurements of voltage and current. Make sure they are well spaced for a good graph. We will increase the voltage up to a maximum of 5V, in 0.5V increments. As you collect the data, you may find that you need to adjust the settings on your meters, so you do not go off scale. 4. Change the resistance and repeat the above steps. 5. Make a graph of voltage versus current for both sets of data with Excel. Measuring the slope of each line will give you the corresponding resistance. 4
B. Resistance Measurements on a Light Bulb Now we will repeat the measurements on a different resistor, a light bulb. Just like the unknown resistors, the light bulb will constrict the amount of current that can flow through the loop. We wish to see if the light bulb follows Ohm s Law. 1. Set up the equipment just as you did in the previous part, but replace the resistor with the small light bulb. The power should be off when making connections. 2. The power supply should be set for 0 volts. The voltimeter should be on 2 VDC. The ammeter should be connected for 500 ma. Turn on the power. By slowly turning the dial on the power supply, you can adjust the voltage across the resistor. As you do this the current should also change. Make ten measurements of voltage and current. Here you will want more data points at the low voltage range. Collect data for 5 points under 0.5V; the rest should be spread out the rest of the voltage range. We will increase the voltage up to a maximum of 5V. As you collect the data, you may find that you need to adjust the settings on your meters, so you do not go off scale. 3. Make a graph of voltage versus current for the data. Also answer the questions that follow Table 2. 5
IV. DATA Name: Section: Date: Table 1 Unknown Resistors R =? R =? V (V) I (A) V (V) I (A) Slope = (from graph). Slope = (from graph). R =. R =. Table 2- Light Bulb V (V) I (A) V (V) I (A) 6
Does Ohm s Law apply to the light bulb? Does it always apply ( Ohmic ), sometimes apply ( sometimes Ohmic ) or never apply ( non-ohmic )? Explain. (To help guide your eye when studying the graph, you might want to have Excel add a trendline to your plot.) Can you determine the bulb s resistance from the graph, just as you did in the previous experiment with the resistors? If so, what value do you say it is, and are there any limitations on this result? One way you can check the resistance of your bulb is to use the multimeter as a ohmmeter. It has the ability to directly measure the resistance of an object. What does the ohmmeter say the bulb s resistance is? Ω What voltage region does this measured resistance correspond to? 7
IV. ADDITIONAL QUESTIONS 1. Explain how your graphs in Part A show that Ohm's law is valid. 2. Imagine that you are investigating the behavior of a component and one of the tests you do is to measure the current as a function of applied potential difference. The graph of this data looks something like the following sketch. Can this component be considered Ohmic? That is, is its resistance constant? voltage current Where is the resistance greater? In the low voltage regime or high voltage regime? Explain your reasoning. 8
3. Using the ohmmeter, NOT the powered circuit, measure your resistance. (You will likely have to adjust the sensitivity or range of the ohmmeter in order to get a reading that isn t off scale ) What is the value? Measure the resistance across several body parts (hand to hand, index finger to wrist, etc.). Does the resistance vary? If so, what seems to affect it? For your resistance, what amount of current would go through your body if you came in contact with a 120 V potential difference?: It is known that high currents through your body can cause serious injury or death. Here are a few of the typical consequences of different currents. 0.001A Can be felt 0.005A Is painful 0.010A Causes spasms 0.015A Causes loss of muscle control 0.070A Probably fatal 9