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UTC Physics 1040 L SECTION PARTNER(S) OHM'S LAW AND EQUIVALENT RESISTANCES Goals of the experiment: Theoretical background: Circuit Diagrams: STUDENT Procedure (use the back of this page): Pre-lab Report DATE
UTC Physics 1040L Ohm's Law OHM'S LAW AND EQUIVALENT RESISTANCES Objective: To learn basic construction and measurement of electric circuits; also to study Ohm's law and voltage, current, and resistance for DC circuits wired in series or in parallel. Apparatus: DC power supply, resistors, connecting wires, computer with current and voltage probes. Theory: A potential difference (or voltage as it is commonly called) is the difference in electric potential energy for a given charge between two points divided by the charge itself. An analogy may be made between electric potential energy and gravitational potential energy: an object at a certain height accelerates as it moves from a high gravitational potential to a low gravitational potential. Likewise, a positive charge would accelerate as it moves from a point of high electric potential to low electric potential. The potential difference, or voltage, is like the height of a hill. To measure a voltage, you must measure the potential at two different points in a circuit, like to measure the height of an object, you must measure its vertical position at its top and bottom. Thus, a voltmeter measures the potential difference in volts across a circuit component by means of two connections that touch the circuit at different points, but are not directly in the path of current. A voltmeter is indicated on a circuit diagram with the symbol shown in Figure 1. V R= 2= // Rev. 12/14 KBW or A V=IR. Wire Figure 1. Circuit Symbols The flow of a certain amount of charge in time is called current, or I = Aq/At. The SI unit of current is the Ampere, which is the current if one Coulomb of charge (approximately 6.25 x 10¹8 electrons) flows through a point in a wire in one second. Electric charge only moves through a conducting path when there is a potential difference between the ends of the conductor. Analogously, water does not flow unless there is a height difference between the start and finish of its path. In any metallic conductor the only mobile particles are electrons; however, for historical reasons, current in a circuit is defined to be the flow of hypothetical positive charge (called conventional current) from a high potential (+) to a low potential (-). The potential difference provides a so-called "electromotive force" to move the charge through the circuit. The source of this potential difference can be a battery, photocell, or some other power supply. An ammeter (whose symbol is shown in figure 1) is the device used to measure current, and it must be placed directly in the path of charge flow to make the measurement. Note that ammeters are labeled to indicate the proper direction of current flow through them. A reverse flow of direct current (DC) through the meter could destroy it. All materials resist the flow of current through them, requiring work to be done to move the charge through the material. The fundamental relationship between current, voltage, and resistance was discovered by Georg Simon Ohm. The relationship and unit of electrical resistance were both named for him to commemorate this contribution to physics. Ohm's law states: if the temperature and other physical conditions of a metallic conductor are unchanged, the ratio of the potential difference across the conductor to the current is a constant. This constant ratio is the resistance of the conductor (1) If the voltage is measured in volts and the current in amperes, the resistance unit is Ohms (22). An Ohmmeter simply measures the voltage and current and takes the ratio itself. A resistor is any device that dissipates energy when charge flows across it. This includes the small circuit devices we call Experiment Description - Page 1 of 3 Voltmeter Ammeter DC Power Supply L ++ - Resistor
Ohm's Law UTC Physics 1040L resistors in the laboratory and any device that uses electrical power, such as a refrigerator, computer, or flashlight. R₁ V₁ Resistors may be placed in a circuit in different configurations with respect to voltage sources, called series and parallel wiring. In series wiring (see Figure 2), the same current runs through each device. Thus if the current is disrupted at any point in the pathway, no resistor receives current. In series wiring, the voltage supplied by the battery is divided between the resistors. The division of energy between the resistors is only equal if the devices have equal resistance. More current will flow through the path of least resistance. R₂ V₂ Since the same current flows through the series resistors, then V = V₁ + V₂ + V3 = IR₁ + IR₂ + IR₂ = IRS, where Rs is the equivalent resistance in series: 1 1 1 1 ==+ Rp R₁ R₂ R3 R3 V3 Rs = R₁ + R₂ + R3 +.... (3) Figure 2. Three resistors wired in series (left) and in parallel (right). In parallel wiring, resistors are connected in such a way that the same voltage is applied across each device. In this case, the current splits in its pathway and branches at junctions, so that part of the current travels through one part of the circuit and another part travels through a different conducting wire. If the path is broken along one path, current still flows through the alternate pathway. Each resistor receives current produced by the voltage supply as if the other resistors were not present. The total current from the battery must be the sum of all the currents that travel through each resistor, or I = 1₁ + 1₂ + 1₂ = V / R₁ +V/R₂ +V/R₂ = V(1/R₁+1/R₂ + 1/R₂) = V(1/Rp), where Rp is the equivalent resistance for the resistors in parallel. +... 2. With the power supply turned off, connect the power supply, an unknown resistor from the resistor board, wires, and probes as shown in Figure 3. You can use any of the resistors B-E, but do not use resistors A or F. The four DC supply Rev. 12/14 KBW Since the current drawn from the battery is greater for multiple resistors in parallel than it is for a resistor alone with the same voltage, a smaller equivalent resistance is implied. The smallest resistance has the largest impact on the equivalent resistance for resistors in parallel. Procedure and Data Analysis: PART I. Ohm's Law for Individual Resistors. 1. On the computer, open Logger Pro. Under the File menu, open the file "Exp 22 Ohm's Law" from the "Physics with Vernier" folder. A graph of potential vs. current will be displayed. The meter window displays potential and current readings. The program will tell you where to plug in the current probe and voltage probe to the green interface box. m Experiment Description - Page 2 of 3 Current probe TO 1₂ R₂ O 13 R3 00 00 Resistor Panel (4) Voltage probe Figure 3. Equipment set up for Ohm's Law. The circuit diagram for the same set-up is shown in the inset.
UTC Physics 1040L resistors have approximate values of 102, 502, 1209 and 5002, in no particular order. Take care that the positive lead from the power supply and the red terminal from the current and voltage probes are connected as shown. Ohm's Law 3. With the power supply turned off, you need to zero all sensors. Click the "Zero 0" button on the toolbar. A dialog box will appear. Click Zero all sensors. This sets the zero for both probes with no current flowing and no voltage supplied. 4. Make sure the power supply is set to 0 V. Turn it on. Click the Collect button on the toolbar to start taking data. Monitor the voltage and current. When the reading is stable click Keep. 5. Increase the voltage on the power supply by approximately 0.5 V. When the reading is stable, click the Keep button. Repeat this process until you reach a supplied voltage on your power supply of 5 V. Do not go over 5 V. When your data is collected, click the stop button and set the power supply back to 0V . PART II. Resistors in Series and Parallel. 1. Using the values of resistance for your three unknown resistors, find their theoretical equivalent resistance in series, Rs, using equation 3. Rev. 12/14 KBW 6. On your graph, adjust the scale so that the data is approximately diagonal. You can do this by clicking the "Autoscale" button or changing the value on the axes yourself by clicking on the last tick mark value for an axis and typing in the maximum value you want displayed on that axis. On the Analyze menu, click Curve fit. Choose a linear equation to fit your data. Record the slope and the y-intercept with their uncertainties for the regression line on your data sheet. Ensure that the y and x axes have proper labels with units, and change the title of the graph to "Voltage vs. current for Resistor _" (whichever one this corresponds to). Print the graph to include in your report. 7. Repeat steps 3-6 for two other resistors on your resistor panel. Make sure to record the values for slope and intercept on your report page, however, you do not need to print the graph for these. 2. Connect the same three resistors that you used in part I so that they are wired in series, as shown in figure 4. from current probe 00 from current probe 0--0 to of 00 to negative terminal. to negative terminal Figure 4. Resistors wired in series (left) and in parallel (right). 3. Using the same method as in part 1, measure the equivalent resistance for the resistors in series. 4. Repeat steps 1-3 for a parallel connection of the three resistors, such as shown in figure 4. When calculating Rp by equation 4, remember to take the reciprocal of your sum of reciprocals. Organize your completed report in the following order: 1. Pre-lab. 2. Neatly written experimental data page with sample calculations and discussion. Remember the units. 3. Your results paragraph. 4. Printed graph from Logger Pro for first individual resistor measured.