Resistance Measurements

Transcription

1 esistance Measurements OBJETE To understand the relationship between the current, voltage, and resistance in a circuit. To study series and parallel resistance circuits. NTODUTON esistance of an electrical element is defined by =/ or =ρl/, where is the resistance of the circuit element, is the potential drop across the element, is the current passing through the element, ρ is the resistivity of the elements material makeup, L is the length of the element, and is the cross-sectional area of the element. There are several ways to measure the value of the resistance; the most direct of which is to measure the potential drop and the current of the element with the aid of a voltmeter and ammeter. dditionally, more than one resistor can be part of a circuit. The resistance may be in a series or a parallel combination. Both of these methods will be studied and applied to the determination of several unknown resistors, series combinations, and parallel combinations. PPTUS o computer o ernier computer interface o Logger Pro o one ernier urrent Probe o one ernier Differential oltage Probe o wires o three known resistors & one unknown resistor o adjustable 5-volt D power supply THEOY s previously stated, resistance [Ω] of any circuit element is given by: = Equation 1 Where, [] is the electric potential between two points across the element and [] is the quantity of charge moving through the element in a unit time. resistor generally obeys this relationship over a wide range. However, it can vary by approximately ±10% from the known value of the resistor; somewhat due to temperature variations of the resistor itself. We call this the precision of the resistor. esistance Measurements - Page 1

2 s the name suggests, a resistance device is one which "resists" the flow of charges in an electrical circuit, thereby reducing the current flow in the aforementioned circuit. n general, the resistance of any material is given by: L = Equation 2 Where, ρ [Ωm] is the resistivity of the material {varies based on what the material is made of}, L [m] is the length of the material, and [m 2 ] is the cross-sectional area of the material, through which the current flows. esistors may be connected in a circuit to either increase their resistance (series combination) or to decrease their resistance (parallel combination). series connection of resistors, B, & is illustrated in Figure 1 below. B Figure 1 B s indicated, the current flows through the resistors, thus, each resistor has the same value of the current. However, as the potential difference is measured across each resistor, each resistor will have a different potential drop (voltage). The total voltage is, thus: TOTL = + Equation 3 B + Using this relationship, Equation 1, and the statement that the current through each resistor is the same yields: = = ( TOTL TOTL EQ SEES + B + + B + ) = = esistance Measurements - Page 2 Equation 4 This defines the relation that the equivalent resistance of a series combination is the sum of the given resistance elements. B B

3 parallel combination of resistors, B, & is illustrated in Figure 2 below. B B Figure 2 n the parallel combination, the resistors are all connected to the same potential difference and, thus, each has the same voltage across them. However, as the current approaches the junction of the three resistors, it must split, and a fraction of the total current passes through each of the three resistors. Thus, the total current in the circuit is given by: TOTL = TOTL TOTL 1 = EQ PLLEL + Equation 5 B + Using this relationship, Equation 1 and the statement that the voltage across each resistor is the same yields: = + + B ( + + ) B = + + B = + + B Equation 6 This gives the relation that the equivalent resistance of a parallel combination is the inverse of the sum of the inverses of each of the given resistance elements. esistance Measurements - Page 3

4 oltmeter-mmeter: The most direct way to determine an unknown resistance, or to verify the series/parallel relationships, is to measure the actual current passing through the system and voltage across the resistor (Ohm's Law). s indicated, a voltmeter (potential difference measuring device) must be connected across the resistor (in parallel) in order that is measures a difference from one side to another (again, the potential difference) and an ammeter (current measuring device) must be connected along the same part of the circuit that passes through the resistor (in series) in order to measure the current actually passing through the resistor; the ammeter does not keep any of the current nor does the resistor so it does not matter if the ammeter is placed before or after the resistor only that it be in-line with it. Figure 3 below is an illustration of this type of measuring arrangement. Figure 3 esistance Measurements - Page 4

5 NTL SETUP With the equipment you have available, a current probe will serve as the ammeter in the circuit and a differential voltage probe will serve as the voltmeter in your circuit.. onnect the urrent Probe to hannel 1 and the Differential oltage Probe to hannel 2 of the computer interface. B. Open the file 22 Ohms Law in the Physics with ernier folder. graph of potential vs. current will be displayed. The meter displays potential and current readings.. With the power supply turned off, connect the power supply, one of the known resistors, wires, and clips as shown in Figure 3. Take care that the positive lead from the power supply and the red terminal from the urrent & oltage Probe are connected as shown in Figure 3. Note: ttach the red connector of the voltage probe closer to the positive side of the power supply. D. lick. dialog box will appear. lick to zero both sensors. This sets the zero for both probes with no current flowing and with no voltage applied. This can have consequences in making the y-intercept 0; or = * +?. E. Have Dr. rts check the arrangement of the wires before proceeding. EXPEMENTL POEDUE a) With one of the known resistors in place, adjust the power supply to approximately 0.5 D. b) Monitor the voltage and current. lick to allow the & probes to talk to the computer. When the readings are relatively stable click. c) ncrease the voltage on the power supply to approximately 1.0 D. When the readings are stable click. d) ncrease the voltage by approximately another 0.5. When the readings are stable click. epeat this process until you reach a voltage of approximately 5.0. e) lick and set the power supply back to 0. ndicate a best-fit-straight-line on the graph and compute the slope and y- intercept. t this point you will want to print ONLY your graph (NO data tables). o Be sure your graph has a clear title indicative of the resistor(s) connected. o uto scale the graph before printing! esistance Measurements - Page 5

6 f) onnect the second of the known resistors and repeat a-e. g) onnect the third of the known resistors and repeat a-e. h) onnect the unknown resistor and repeat a-e. i) Using your knowledge of resistor combinations, predict how series resistors would affect current flow. o What would you expect the effective resistance of two equal resistors in series to be, compared to the resistance of a single resistor? j) onnect the three known resistors in series and repeat a-e. s shown in the illustration, be sure to connect the voltmeter across the combination, not across the individual resistors. esistance Measurements - Page 6

7 k) Using your knowledge of resistor combinations, predict how parallel resistors would affect current flow. o What would you expect the effective resistance of two equal resistors in parallel to be, compared to the resistance of one alone? l) onnect the three known resistors in parallel and repeat a-e. s shown in the illustration, be sure to connect the voltmeter across the combination, not across the individual resistors. esistance Measurements - Page 7

8 OE PGE EPOT TEMS (To be submitted and stapled in the order indicated below) (-5 points if this is not done properly) ompleted Laboratory esponsibility and over Sheet DT (0 points) ll data collected was in the form of graphs DT NLYSS (0 points) ll data analysis will be graphical analysis GPHS (worth up to 10 points) Three known resistor graphs One unknown resistor graph One series combination graph One parallel combination graph GPH NLYSS (worth up to 40 points) The answers to the questions below should be completed on the back of each respective printout For EH of the known resistances: re the results that you found in each of these trials consistent with what you expected to find? s there a specific relationship between the variables (,, & ) or only a general one? Based on your graph of vs. for each resistor: o Explain the significance of the slope. What should it be? o How would you expect the slopes of the graphs of each of the resistors individually to look in comparison to each other? Based on your data and graphs, do your resistors follow Ohm s law? Explain. esistance Measurements - Page 8

9 For the unknown resistor: What does your data indicate as to the value of your unknown resistor? Within the errors you found for your other resistors and combinations (± the actual percentage values), what do you feel is the range in which your resistor would most likely fall? Based on your graph of vs. for this resistor: o Explain the significance of the slope. Based on your data and graph, does your unknown resistor appear to follow Ohm s law? Explain. For the series combination: Do the values ( vs. ) of the series combination, in theory, correspond to your expectations; i.e. in comparison to any of the individual resistors, what expectation about the collected data did you have? Explain any variations. Based on your graph of vs. for this resistor: o Explain the significance of the slope. What should it be? Show this calculation on the back of the graph. Based on your data and graph, does your series combination appear to follow Ohm s law? Explain. For the parallel combination: Do the values ( vs. ) of the parallel combination, in theory, correspond to your expectations; i.e. in comparison to any of the individual resistors, what expectation about the collected data did you have? Explain any variations. Based on your graph of vs. for this resistor: o Explain the significance of the slope. What should it be? Show this calculation on the back of the graph. Based on your data and graph, does your parallel combination appear to follow Ohm s law? Explain. ONLUSON (worth up to 20 points) See the Physics Laboratory eport Expectations document for detailed information related to each of the four questions indicated below. 1. What was the lab designed to show? 2. What were your results? 3. How do the results support (or not support) what the lab was supposed to show? 4. What are some reasons that the results were not perfect? esistance Measurements - Page 9

10 QUESTONS (worth up to 20 points) DO NOT forget to include the answers to questions that were asked within the experimental procedure 1) t was stated that the voltmeter (differential voltage probe) must be placed in parallel with the resistor in order to measure the potential difference across the resistor. However, the voltmeter, by the very nature that it is an electrical device, also has resistance. What then, qualitatively speaking (really big, really small, doesn't matter, etc.), must the resistance of the voltage probe be so as not to adversely affect the operation of the circuit? onsider the parallel resistance equation as you attempt to answer the question!! 2) t was stated that the ammeter (current probe) must be placed in series with the resistor in order to measure the current passing through the resistor. However, the ammeter, by the very nature that it is an electrical device, also has resistance. What then, qualitatively speaking (really big, really small, doesn't matter, etc.), must the resistance of the current probe be so as not to adversely affect the operation of the circuit? onsider the series resistance equation as you attempt to answer the question!! 3) How do you suspect that the lights, T, appliances, etc. of your home are connected; in series or in parallel? Explain your reasoning. esistance Measurements - Page 10