Lab 8: Resistance, Series Circuits and Lights Out! Introduction: The Coulomb force on an electron in a field is qe. Though we have studied charges and fields in free space, the same fundamental physics applies to the charges and fields in electrical circuits all around us. If there is an electric field across a conductor, the charges in the conductor will move because of the Coulomb force. However, unlike free space, electrons in conductors are immersed in atoms 10 22 atoms/cm 3 to be exact. With all these atoms, a moving electron is bound to undergo many collisions as it is moves under the influence of the electric field. This collision process, and the loss of energy, is the reason behind the resistance of a conductor. Ohm s Law is a simple relationship that relates the amount of charge flow (current = I = q / t) to the electric field forcing the charge, and the resistance stopping the charge movement. By the end of this lab you should: Understand Ohm s law (I = V / R) Use a meter to measure voltage and current. Apply Ohms law to series circuits Materials: Variable power supply (Ground 0VDC, ±5VDC or ± 6VDC, ±12VDC) Banana plug leads and alligator clips Flow apparatus with tubes Digital multimeter Four AAA cells, one D cell, and a 6V flashlight bulb. Resistive carbon wire on a meterstick 1
Experiment 1: Fields and charge flow in wires. Charges will move if there is an electric field present. Since V = E dl a electric field can be created in a conducting wire by just putting different potentials at the wire ends, that is E = V/l in Volts/m units, where l is the length of the wire. In this experiment, you will study the current and electric fields in a wire. Begin by putting the wire at a potential of about 1 V as shown in Figure 1. Measure the voltage at various points along the wire. What do you find? Think about what that means and enter your thoughts and findings in your notebook. Use these observations to quantify the electric field (what is its value in the wire?) and the movement of charges in the wire. Remember voltages must always be measured from a reference point, i.e. V b - V a. Use the ground on your power supply as your common reference for this activity. b V a b, an Now, connect the two ends of the wire to a different potential. For safety, don t use more than a 5 V difference. Measure the voltage at several regular points along the wire and use these measurements to quantify the electric field, and movement of charges in the wire. Using alligator clips, change the potential at various points along the wire. Using your power supply, place different potentials on the wire. An example setup with three potentials is shown in Figure 2. Measure the potential along the wire and plot out the electric field strength along the wire. The e-field and Coulomb force pushing on the charges at each point in the wire has to be scaled because it is in a wire rather than in vacuum. The fields and forces along the wire, however, can be determined relative to one another accurately. Figure 1: Spark plug wire has a high resistance to let us do the experiment without too much current. In the figure, the wire is set to a constant potential, why does the meter not measure any voltage difference? 2
Experiment 2: Resistance when charges collide Life in a conductor is very crowded, the mean free path before an electron hits one of the billions upon billions of neighboring atoms it is less than a nanometer. Therefore, an electric field in a wire never gets to accelerate an electron to a very high speed before the kinetic energy of the electron is transferred to the conductor by another collision with a nearby atom. At any point in the conductor the kinetic energy of the conductors is basically zero, not (V b -V a ) q as would be expected in free space. In analogy with the conductance of a liquid through a conduit, the flow of electrons depends on the force you apply (Eq) and the resistance (R) of the pipe it flows through. The concept of the resistance of a conductor to the flow of conductors can be observed clearly with liquids flowing through conduits. You will be given a set amount of water (symbolizing charge) raised in a gravitational potential, mgh (representing the electrical potential), and several tubes for the water to flow when the end of the tube is placed at a lower gravitational potential energy point. A picture of your setup is shown in the figure. You will be given four types of conduits. A thin conduit, a medium area conduit, a long medium area conduit, and a large area conduit. With the long medium conduit, once the water starts flowing try moving the coil of tubing all around in many directions, keeping the end of it in the same location. Does the flow depend upon the path or the initial and final potential of the tube? Write in your notebook your observations for fluid flow in the different types of conduit and give a full analogy for the flow of electrical current through different types of conductors. You will have a stopwatch to time the flow of the liquid. Make sure to describe the comparison between the gravitational potential and electrical potential. Figure 2: Several potentials attached to a wire being measured with a voltmeter. Figure 3: Setup of the flow apparatus with the medium tubes both long and short. 3
Experiment 2: Build your own flashlight "What's wrong with the carbide lantern?" Before Chris could reply to Pat's question, darkness descended. "Great! I've been begging my folks for a new lamp since the last time we went caving. Too late now! Let's fire up one of our candles." It took a bit of rummaging through the pack to find a match and candle in the shroud of darkness. Finally Pat struck a match, but it flickered out. This happened again with the second match, and the third. The reason suddenly occurred to Chris. "You've gotta be kidding me -- I think the air is bad down here! The guidebook didn't say anything about that, did it?" "Not that I remember. You know, my breath is a little short now that you mention it." We need to get out of here right now. Shine your flashlight over here while I take another look at the map." Pat rifled through his pack in the darkness. "Bad news Chris I left the flashlight on the ground where we ate lunch. All I ve got is this spare D battery!" Beautiful! We walked for three hours since lunch, and we can't make it back there without a light! Okay, lets calm down. Getting upset won t help anything." "OK. OK. You re right. What do we have for a light?" "I have a spare bulb for my lantern. But I didn't bring a spare battery." My pager has one AAA cell." "Weird, I've got my pager too. It has a AAA cell as well. Why do we bring these along? "Good thing we did! But the lantern bulb is for 6 V. Do you think it will work with two AAA and a D cell?" "Even if it does it won't be as bright, and the batteries may not last long enough for us to get out. I'm starting to get worried..." Hey, you had physics last term! You studied circuits right? You had the lab. What should we do?" 4
The Exercise: 1. Your group will have available two AAA cells, 1 D cell, and a 6V bulb. In the lab you will have available a multimeter, lengths of wire, and electrical tape. Some information that you will need for this lab is that when 6V is applied to the bulb, it draws 0.2A and when 12 V is applied, it draws 0.4A. Determine the resistance of the bulb from this information and record it in your notebook. The internal resistance/impedance and of the alkaline AAA and D cells is about 0.2 Ohms 2. This information on the discharge characteristics can be found on the websites of any of the major battery manufacturers. Your goal is to find a workable arrangement of the batteries so that the bulb could shine for at least 3 hours, thus allowing the two unfortunate spelunkers to reach safety. Calculate the current through each of the batteries for the various parallel and series battery configuration options, e.g. AAA in series with D, AAA in parallel with each other and in series with D, all batteries in parallel, etc. Given the lifetime of each battery at these current drains, will they last? Report in your notebook the battery configuration that will have the most output power and last for three hours. Additional Resources: www.duracell.com/oem/primary/alkaline/alkaline_manganese_tech.asp www.physics.udel.edu/~watson/scen103/battdata2.html www.physics.udel.edu/~watson/scen103/battdata1.html 5