1、Functional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 1 9/27/2018USER MANUAL FOR VOLTAGE DIVIDERFunctional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 2 9/27/2018TABLE OF CONTENTS1. INTRODUCTION .42. THEORY AND PREDICTIONS5
2、3. WIRING INSTRUCTIONS104. APPARATUS .105. TESTING SEQUENCE.106. LIST OF PARTS137. REFERENCES 15Functional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 3 9/27/2018LIST OF FIGURE CAPTIONSFigure 1 - (a) Voltage divider circuit without load potentiometer, but a sign
3、al wire; (b) the voltage divider circuit with a load potentiometer.Figure 2 Theoretical and experimental variation of output voltage, , with resistance outVratio, , for =5.18V.21RinVFigure 3 - Picture of function module in which the locations of the output voltage terminals, input voltage terminals,
4、 ground and the potentiometer are shown.LIST OF TABLE CAPTIONSTable 1 - Wiring of Voltage DividerTable 2 - Apparatus Needed for TestingTable 3 - Testing Sequence of and , without a load resistance, for =5.18V.1R2 inVTable 4 - List of Required ComponentsFunctional Module Report Voltage Divider Alexan
5、der Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 4 9/27/20181. INTRODUCTIONVoltage division is a method used to change the voltage across a particular circuit through the use of resistors as the only circuit component. The voltage divider uses two resistors in series to decrease the voltage through a p
6、arallel circuit, according to the second resistor. Figure 1a shows the circuit diagram for a voltage divider in open circuit configuration. When this second resistance is equal, the voltage through the circuit should be halved. With the values of resistances different, the output voltage will differ
7、. The input voltage, , the output voltage, , and the two variable resistances, and , inVoutV1R2are indicated. Figure 1b shows a voltage divider with a potentiometer acting as two variable resistors. This particular open circuit has many applications in which the voltage across another circuit needs
8、to be varied. As the variable lead on the potentiometer changes the resistance of the two variable resistors change. In this manual, we will investigate the influence of resistance on this voltage divider configuration, in order to decrease potential with precision, and the relationship between the
9、output voltage as a function of the resistance ratio R2/R1.Functional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 5 9/27/2018outVinV1R2Figure 1 (a) Voltage divider circuit without load potentiometer, but a signal wire; (b) the voltage divider circuit with a pote
10、ntiometer acting as both resistors.2. THEORY AND PREDICTIONSIn a series circuit, in which the same current flows through all of the components, the total resistance is equal to the sum of the resistance of each of the resistors. In addition, the sum of individual voltage drops across each resistor i
11、s equal to the total voltage applied to the circuit. This is often referred to as Kirchoffs Voltage Law (Rizzoni, 2000).According to Ohms law, if the voltage is constant and the resistance is changed, the current must change as well. Adding a load resistor in parallel onto the signal wire will influ
12、ence how the current flows through the circuit. The parallel resistors cause a split in the current, which favors the side with less resistance, or greater load. Therefore, Functional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 6 9/27/2018all three resistances i
13、nfluence the division of voltage in a parallel section of circuit with a load rheostat. This is Kirchoffs Current Law.To derive the Voltage Divider Rule for an open, series circuit, we begin Ohms law:(1)IRVAccording to Kirchoffs Voltage Lawin accordance with Ohms Lawthere are two distinct voltages t
14、hat vary according to two distinct resistances in series. Equations 2 and 3 show this relationship.(2)IRV1(3)2From Kirchoffs Voltage Law, we can know that the sum of each individual voltage is equivalent to the total voltage of the circuit (Equation 4). From these three equations, we can then make a
15、 series of algebraic calculations to determine the Voltage Divider Rule.(4)21V(5)IR)(6)21IThus,(7)212RVVout (8)inout21Functional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 7 9/27/2018Essentially, in Equations 7 and 8, the voltage flowing out of a voltage divide
16、r is equivalent to the ratio of the secondary resistance to the sum resistance, times the input voltage, or the inverse of the ratio of the resistors times the input voltage. Instead of relying on a single resistance to split the voltage, the voltage divider relies upon the properties of two resista
17、nces in series.Figure 2 shows a plot of Equations 7 and 8 for = 5V and between 0 and inV21R15. When variable resistors are used , the voltage can be changed through the ratio of outthe two resistances. We can see that when the two resistances are equal (i.e., when =1), the voltage is cut in half acc
18、ording to Equation 8. When the ratio is greater 21Rthan one (i.e., when the first resistance is greater than the second), the voltage is smaller than one half. If the ratio is less than one (when the second resistor is greater than the first), then the divided voltage will be more than one half. For
19、 =0, the output voltage 1Requals the input ( = ).outVinFunctional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 8 9/27/201801234560 1 2 3 4 5 6 7 8R1/R2Output Voltage (V)Data PointsTheoretical LineFigure 2 Theoretical and Experimental variation of output voltage,
20、, with outVresistance ratio, , for =5.18V.21RinVIn this graph, Figure 2, it is easily seen that the measured relationship between the output voltage with respect to ground as a function of the ratio of the resistances R1/R2 is a decreasing function that approaches zero as the resistance ratio R1/ R2
21、 approaches infinity. Thus, for a resistance ratio in which R1 is R2, the output voltage would be very low compared to the input voltage, and for a resistance ratio in which R2 is R1 the output voltage would be very close to the input voltage.Functional Module Report Voltage Divider Alexander Kloth7
22、8b5bd47bfa2da92dca2463c07b957ae.pdf 9 9/27/2018The mathematical function that is the representation of this particular equation is shown below where y is the output voltage, Vout, and x is the ratio of resistances, R1/ R2.(9)yin1It is very important to note that the voltage decreases as a function o
23、f equation (8). In figure 2, equation (8) was the function used to plot the theoretical line. As easily inferred in the following graph the data closely models the mathematical function of equation (8). The average percent error of the output voltage for all data points was 5.15%, and the standard d
24、eviation from this average percent error was found to be 5.61%. Some possible causes for error may be due to the fluctuation of the digital multi-meter reading when used to measure the resistance and voltage across the circuit, the uncertainty caused by the lead connections when measuring the voltag
25、e output. However, the overall uncertainty caused by these two problems is relatively small. To decrease the uncertainty of these to causes it is recommended that you allow ample time for the multi-meter to “settle” on the appropriate resistance or voltage value instead of taking a reading while the
26、 multi-meter is fluctuating. Also, when measuring the voltage and resistance make sure that the leads are touching the wires in the circuit the instant when you record the measurement. Table 3 in the testing and sequences section contains all of the data in figure 2.Functional Module Report Voltage
27、Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 10 9/27/20183. WIRING INSTRUCTIONSTable 1 Wiring of Voltage DividerRed (+5 volts) to inV1Rto yellow (signal), to 1R2Black Ground (0 volts)to ground (0 volts)2to ground (0 volts)LRYellow In Circuit 1, signal wire ( )outVIn Circuit 2, to L4.
28、APPARATUSTable 2 Apparatus Needed for TestingDigital multimeter, or equivalent ohmmeter and voltmeterPower sourceVoltage box, with ground (0 volts) and +5 volt outletsFunctional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 11 9/27/20185/64” flathead screwdriver5.
29、 TESTING SEQUENCEAdjust the potentiometer such that the resistance between the input terminal and the variable lead is at an absolute minimum which should be around 100 ohms. Measure and record the exact value of this resistance with the multimeter, and then connect the potentiometers to the circuit
30、 if not already connected. Then connect the power source to the circuit by connecting the +5V the +5V source and the ground terminal to the ground source. Once the power source is giving voltage to the circuit , read the voltage of the signal wire with the multimeter, which should yield an approxima
31、te result. Next, change the potentiometer resistance slowly such that 20 measurements of resistance between the input terminal and the variable lead or the output terminal and the variable lead, and 20 corresponding voltage measurements should be taken as well. Try to take these measurements in such
32、 a way that the resistance is in equal increments throughout the entire range of the potentiometer. It is imperative that you disconnect the voltage supply from the circuit when measuring the resistance between the terminals. Also, when taking these measurements make sure that the multi-meter is not
33、 fluctuating when the measurement is taken and that the leads of the multi-meter are making contact with the circuit the instant the measurement is taken. Table 3 describes the expected results when the voltage divider that lacks a load resistance is tested, when =5.18V. Figure 2 shows inVthe graph
34、of the test data, and figure 3 contains a picture of the function module.Functional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 12 9/27/2018Table 3 Testing Sequence of and , without a load resistance, for =5.18V.1R2 inVTrial Vout R2 R1 R1/R2Vout Theoretical% Err
35、or of Vout1.000 0.000 0.106 261.894 2468.369 0.002 0.0002.000 0.120 7.460 254.540 34.121 0.147 0.0813.000 0.250 13.570 248.430 18.307 0.268 0.1004.000 0.380 20.300 241.700 11.906 0.401 0.1795.000 0.490 25.600 236.400 9.234 0.506 0.1756.000 0.620 32.600 229.400 7.037 0.645 0.3497.000 0.740 38.600 223
36、.400 5.788 0.763 0.4008.000 0.870 45.200 216.800 4.796 0.894 0.4939.000 1.010 52.400 209.600 4.000 1.036 0.65010.000 1.120 57.800 204.200 3.533 1.143 0.64411.000 1.240 64.600 197.400 3.056 1.277 1.21812.000 1.360 69.200 192.800 2.786 1.368 0.29313.000 1.490 76.000 186.000 2.447 1.503 0.51514.000 1.6
37、20 83.500 178.500 2.138 1.651 1.44415.000 1.760 91.200 170.800 1.873 1.803 2.30216.000 1.860 96.600 165.400 1.712 1.910 2.91317.000 2.000 102.700 159.300 1.551 2.030 1.96518.000 2.120 108.500 153.500 1.415 2.145 1.77819.000 2.240 115.000 147.000 1.278 2.274 2.63420.000 2.360 121.400 140.600 1.158 2.
38、400 3.47121.000 2.490 127.500 134.500 1.055 2.521 2.92022.000 2.620 134.700 127.300 0.945 2.663 4.56623.000 2.750 140.400 121.600 0.866 2.776 2.98424.000 2.870 147.100 114.900 0.781 2.908 4.90525.000 3.000 153.400 108.600 0.708 3.033 4.64326.000 3.120 159.900 102.100 0.639 3.161 6.48127.000 3.250 16
39、6.400 95.600 0.575 3.290 6.94428.000 3.370 172.100 89.900 0.522 3.403 6.238Functional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 13 9/27/201829.000 3.490 179.300 82.700 0.461 3.545 11.91130.000 3.620 184.900 77.100 0.417 3.656 8.55131.000 3.750 191.600 70.400 0
40、.367 3.788 10.37532.000 3.870 197.500 64.500 0.327 3.905 10.64733.000 4.000 203.000 59.000 0.291 4.014 4.64934.000 4.130 210.000 52.000 0.248 4.152 8.84835.000 4.250 216.000 46.000 0.213 4.271 9.64236.000 4.370 222.000 40.000 0.180 4.389 10.63437.000 4.500 229.000 33.000 0.144 4.528 19.12338.000 4.6
41、20 234.000 28.000 0.120 4.626 5.35939.000 4.740 241.000 21.000 0.087 4.765 28.47140.000 4.870 246.000 16.000 0.065 4.864 9.74141.000 5.000 253.000 9.000 0.036 5.002 5.79442.000 5.120 259.000 3.000 0.012 5.121 5.93143.000 5.180 262.000 0.000 0.000 5.180 DNEFunctional Module Report Voltage Divider Ale
42、xander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 14 9/27/201801234560 2 4 6 8 10 12 14R1/R2Output Voltage (V)Data PointsFigure 2 Experimental variation of output voltage, , with resistance ratio, , outV21Rfor =5.18V.inVFunctional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c0
43、7b957ae.pdf 15 9/27/2018Figure 3 Picture of function module in which the locations of the output voltage terminals, input voltage terminals, ground and the potentiometer are shown.Functional Module Report Voltage Divider Alexander Kloth78b5bd47bfa2da92dca2463c07b957ae.pdf 16 9/27/20186. LIST OF PART
44、STable 4 List of Required ComponentsPiece ResistancePotentiometer 0.1-262 kRed wire Not applicableBlack wire Not applicableYellow wire Not applicableBreadboard Not applicable7. REFERENCESCUNNINGHAM, David R., SUTTLER, John A. (1991) Basic Circuit Analysis. 1st edition. Boston, MA. Houghton Mifflin, 1991, pp. 78-83, 94-95, 111.RIZZONI, GIORGIO. (2000) Principles and Applications of Electrical Engineering. 3rd edition. Boston, MA. McGraw-Hill, 2000, pp. 30-48.
