Current, resistance, and Ohm s law Apparatus DC voltage source set of alligator clips 2 pairs of red and black banana clips 3 round bulb 2 bulb sockets 2 battery holders or 1 two-battery holder 2 1.5V (D) batteries 3 10-Ω resistors (brown-black-black 1 51-Ω resistor (green-brown-black 1 100-Ω resistor (brown-black-brown 1 39-Ω resistor (orange-white-black Goal To determine the relationship between current and resistance in an electric circuit for a simple DC circuit with a battery and resistor. Introduction Let s review some important ideas from lecture and previous labs. 1. a circuit is a closed loop of conductors from one terminal of a battery to another terminal of a battery. Current does not flow in a circuit unless the circuit is a closed loop. 2. a DC circuit refers to a circuit that contains a battery (or power supply) that maintains a constant potential difference across its terminals and thus creates a constant current in the circuit. 3. the battery creates a surface charge gradient around the circuit. The surface charge on the conductor(s) (i.e. wires ) creates a uniform electric field within the conductor(s) (hereafter referred to generally as wires ). 4. electrons flow through the battery from the positive terminal to the negative terminal of the battery and flow opposite the direction of the electric field within the wires. 5. the rate that electrons flow in the wires is called the electron current. 6. the conventional current (in coulombs/second, or amps) is opposite in direction to the electron current. 7. resistance (of a wire or filament, for example) is resistance to flow or resistance to current meaning that for a given electric field in a wire, the greater the resistance of the wire, the less the current. Resistance is due to collisions of mobile electrons within the conductor as they move through the conductor. More collisions results in a greater drag force which results in a greater resistance to flow. It is this last claim that we will investigate in more detail in this experiment. observations, and questions below, explain your reasoning. For all experiments, A single bulb circuit Consider the single-bulb circuit shown in Figure 1. 1
Figure 1: A battery and a single bulb. Does the current start out high when it leaves the battery and then decrease as it goes through the bulb so that there is less current going back to the other side of the battery? Or, is the current flowing through the circuit the same everywhere? Draw and label an arrow showing the direction of the electric field at a location in the filament. Draw and label an arrow showing the direction of current through the battery and draw and label an arrow showing the direction of current through the resistor. 1. Predict what you think the current is in different parts of the circuit shown in Fig 1. How does the current at point 1 compare to the current at point 2? 2. Now, actually set up the single-bulb circuit. For this activity we are going to use a multimeter. A multimeter is capable of measuring many different things including current, voltage, and resistance. Right now, we are going to use it to measure current. To prepare the meter to read current, follow the steps below: (a) Make sure the black lead is plugged into the black port labeled COM at the bottom of the meter. (b) Plug the red lead into the red port labeled A. (c) Turn the dial so that the arrow head lines up with the yellow 20 in the range labeled DCA which stands for DC Amps. This is in the lower left section of the dial. (d) Make sure it is NOT set to the white 20 just above the yellow 20. 2
(e) Press the power button in the top right corner of the meter to turn it on. It should now be ready to measure current. When the multimeter is set up to measure current, we will refer to it as an ammeter. 3. In order to measure the current in a circuit, the current must actually flow through the ammeter. This means that we have to insert the ammeter into the circuit. (a) First, disconnect the wire from one side of the battery. Your circuit will now be open and the bulb not be lit. (b) Take the wire that you just disconnected and clip it onto the tip of one of the leads coming from the ammeter. (c) Take the other lead coming from the ammeter and connect it to the battery. You can just hold the tip of the lead onto the bare wire coming out of the battery holder, or you can use another alligator clip wire to connect them. (d) You should now notice that the bulb is lit again. This is because you have reestablished a complete circuit. It s just that now the ammeter is part of the circuit. 4. Read the value of the current on the display and record it below. Is the value + or? Record the sign as well. The unit of current is the ampere (A), named after the French physicist Andre-Marie Ampere. Sometimes we just say amps for short. This unit tells us how much charge is flowing past a single point in the circuit every second. One amp is defined as one coulomb of charge per second. 1 A = 1 C 1 s A current of 1.0 A means that if you look at one point in the circuit, 1.0 C of charge is flowing past that point every second. A current of 2.0 A means that 2.0 C of charge are passing by every second. 5. Not only can you tell how much charge is passing a point, you can also tell in what direction the current is flowing. To do this, you look at the sign of the current on the meter. If the current flows in through the red lead, then through the meter, and out through the black lead, the meter records the current as positive. If, however, the current flows in through the black lead, then through the meter, and out through the red lead then the current is recorded as negative. Looking at the sign of the current you recorded above, did the current flow from the battery, through the meter, and then out to the bulb? Or, did the current flow from the bulb, through the meter, and then back to the battery? If it reads a negative value, you may disconnect the ammeter and reconnect it so that current flows into the red lead and out of the black lead. 3
6. Now, let s use the meter to measure the magnitude and direction of the current at another location in the single-bulb circuit. Measure the current at point 2 shown below. Record your measurements on the picture below by drawing arrows which show the direction of the current at each location, and then write the magnitude of the current next to the arrow. Please ask Dr. Titus to check your work before continuing. Two bulbs in series 1. Connect two bulbs together like those shown in the picture below. Whenever two circuit elements (such as bulbs) are connected together so that there is only one path through the elements (without the path splitting or branching in between the elements), then those elements are said to be connected in series. In other words, when two elements are connected in series, a terminal of one element is connected ONLY to one terminal of another element. How does the brightness of the two bulbs compare with the brightness of the bulb in a single-bulb circuit? 4
Predict what the magnitude and direction of the current will be at various locations in this two-bulb circuit. You can do this by drawing arrows on the figure above. Explain the reasoning used in making your predictions. 2. Use the ammeter to measure the magnitude and direction of the current in the following parts of the circuit: (1) the current entering the first bulb, (2) the current exiting the first bulb and entering the second bulb, and (3) the current exiting the second bulb. Sketch the results on the figure below, just as you did before. The figure should have three arrows. 3. Consider your observations above, and answer the following questions. (a) Does current get used up in the first bulb, or is the current going through the second bulb the same as the current going through the first bulb? (b) In this context, how is the brightness of a bulb related to the amount of current flowing through it? (c) Suppose you think of the bulb as providing a resistance to the flow of current in a circuit, rather than something that uses up current. How do you expect the total resistance in a circuit would be affected by the addition of more bulbs that are connected in series? (d) Formulate a rule for predicting whether current increases or decreases as the total resistance of the circuit is increased. In other words, as the resistance of the circuit increases, the current through the battery (and circuit). (e) When doubling the number of bulbs (from 1 to 2), did the current decrease by a factor of 1 2? 5
Please ask Dr. Titus to check your work before continuing. Two resistors in series The rule you have formulated based on your observations with bulbs is qualitatively correct. It can predict whether the current increases or decreases. But, it will not necessarily be quantitatively correct. That is, it will not allow you to predict the sizes of the currents correctly. The reason is that resistance of a light bulb actually changes as the current through the bulb changes. As a filament becomes hotter, its resistance changes. For this reason, we say that a light bulb is non-ohmic. Another common circuit element, which does not have this problem, is the resistor. A resistor has a constant resistance regardless of how large the current through it is. You will now reformulate your rule using resistors and will make it quantitative. According to Ohm s law for an ideal resistor, V = IR (1) The potential difference V is the difference in electric potential across the resistor. We often call this voltage, and it is generally measured from the + terminal of the resistor to the terminal of the resistor, with the + terminal defined to be the terminal in which positive current flows. 1. To maintain a constant potential difference, set aside your batteries and plug in a voltage source. Connect the green ground terminal of the voltage source to the black terminal of the voltage source (if your voltage source has a green terminal). Connect an alligator clip to the red terminal and an alligator clip to the black terminal. These leads will be the two terminals of your voltage source, like the two terminals of a battery. 2. Using the other multimeter, connect a black lead to the COM port and a red lead to the VΩHz port. Turn the dial on the multimeter to the green DCV 20 setting, which will read up to 20 volts (DC). A multimeter used to measure voltage is called a voltmeter. 3. Connect the leads of the voltmeter across the leads of the voltage source, and measure the potential difference (i.e. voltage) across the voltage source. Turn the dial on the voltage source until the voltmeter reads 1.0 V. 4. Select the resistor which has the colored bands brown, black, black, gold. 5. Using your voltage source, set up the circuit shown below with your voltage source and the resistor. 6
6. Disconnect the circuit and insert your ammeter. Measure the current through the battery and the resistor. (Note: based on your previous experiments, you should realize that the current through the battery and the current through the resistor is the SAME for this circuit.) Record your results below. Current through Resistor A = A. 7. Now, connect another, identical resistor to the first resistor, as shown below. How do you expect this to affect the total resistance of the circuit? How do you expect this to affect the current through the battery (and resistors)? 8. Measure the current through the each resistor in the circuit above. Current through Resistor B = A. Current through Resistor C = A. How does the amount of current produced by the battery in the single-resistor circuit compare to that in the two-resistor circuit when the resistors are connected in series? 7
When you put two light bulbs in series, the current though each bulb was NOT half the current with just one bulb in the circuit. How were your results with the resistors different than with light bulbs? Ohm s Law You will now investigate Ohm s law quantitatively. 1. Obtain a set of resistors. 2. We are well acquainted with how to measure the current flowing through a circuit. But, we need to know how to use the multimeter to measure resistance. Follow the steps below to set up the meter to measure resistance. (a) Make sure the black lead is plugged into the socket labeled COM. (b) Plug the red lead into the red socket labeled VΩHz. (c) At the top of the dial, there is a range of white numbers labeled Ω. There are several settings ranging from 200 up to 20M. Set the dial to 200. (d) Turn on the meter s power switch. 3. The meter is now ready to measure resistance. The units of resistance are ohms and the symbol we use for this is a Greek capital omega (Ω). When the meter is set up to measure resistance, it is usually refered to as an ohmmeter. You should have the following resistors: 3 which have the colored bands brown, black, black, gold 1 which has the colored bands green, brown, black, gold 1 which has the colored bands brown, black, brown, gold 1 which has the colored bands orange, white, black, gold Pick up one of the brown, black, black, gold resistors. Hold the ohmmeter s red lead against one side of this resistor and hold the ohmmeter s black lead against the other side. What reading do you measure? You should measure something close to 10 Ω. All resistors with these colored bands have 10 Ω of resistance. 4. Measure the resistance of the green, brown, black, gold resistor. You should get something close to 51 Ω. If you measure the resistance of the brown, black, brown, gold resistor, you should get 100 Ω. If you measure the resistance of the orange, white, black, gold resistor you should get about 39 Ω. Record your results below. 8
5. Put together (using alligator clip wires) a combination of resistors that would give a total resistance of 20 Ω. Test this combination with the ohmmeter to see if you are right. How did you combine your resistors? Make a sketch below. 6. What combination of resistors would give a total resistance of 71 Ω? Make a sketch below and tell how they are connected. 7. We will now investigate the relationship between current and resistance for a given voltage. 8. Use a voltmeter to set the voltage source at 6.0 V. 9. Connect the circuit shown below and use the ammeter to measure the current through the resistor. Record the current in the data table. Record the measured resistance (or calculated resistance) for each resistor. 10. Repeat for the other resistances shown in the data table. Theoretical Resistance, R (Ω) Measured Resistance, R (Ω) Current, I (A) 39 51 61 71 81 90 100 Table 1: Current vs. Resistance 11. Input your data into Logger Pro, and make a graph of I as a function of R. 12. Fit a curve to the data (Note: according to theory I = V R.) 9
13. Record the equation for the best-fit curve. 14. According to Ohm s Law, what physical quantity does the proportionality constant represent? 15. Compare the proportionality constant from your curve fit to what you measured with the voltmeter. 10
Lab Report Name: Lab Partners: Date: Description of experiment: 1. Suppose that you have a battery connected to resistors R 1, R 2, and R 3 that are connected in series. What is the total resistance of the circuit? 2. A 9-volt battery is connected to a 10Ω resistor and a 20Ω resistor that are connected in series. What is the current through the 10Ω resistor? What is the current through the 20Ω resistor? What is the current through the battery? 3. A battery is connected to a light bulb. You want to measure the current through the light bulb. Describe how you would connect an ammeter to measure the current? 4. A battery is connected to a light bulb. You want to measure the voltage across the light bulb. Describe how you would connect a voltmeter to measure the current? 5. If you graph the current as a function of the voltage for an ideal resistor, what is the slope? 11