General Physics Laboratory II
General Physics Laboratory II PHY 222
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This 18 page Class Notes was uploaded by Ms. Bryce Wisoky on Wednesday October 21, 2015. The Class Notes belongs to PHY 222 at Syracuse University taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/225641/phy-222-syracuse-university in Physics 2 at Syracuse University.
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Date Created: 10/21/15
V DC CIRCUITS f05 01 INTRODUCTION DC stands for direct current A direct current stays the same in magnitude and does not change its direction Ohm7s Law and the rules for effective resistance of resistors con nected in series and in parallel which we studied in the previous experiment can be used to understand only simple DC circuits More general approach which can be applied to analyze any DC circuit is based on so called Kirchhoff7s Rules PURPOSE 0 Experimental veri cation of Kirchhoff7s Rules 0 Analysis of a complex DC circuit with Kirchhoff7s Rules DC CIRCUITS V l PRE LAB ASSIGNMENTS A Readings There are two Kirchhoff7s Rules junction rule The sum of the currents entering any junction must equal the sum of the currents leaving that junction loop rule The sum of the potential differences across each element around any closed circuit loop must be zero The rst rule re ects more general law of charge conservation Net charge cannot disappear or pop out from nothing at the junction The second rule stems from the law of energy conservation Since the electric forces are conservative7 energy done by electric forces on a test charge along any closed loop must be zero Let us apply Kirchhoff7s Rules to the circuit shown in Fig 1 ln fact7 we will study this circuit experimentally as well This is an example of the circuit which cannot be understood from the rules for resistors in series and in parallel h b Figure 1 DC circuit analyzed in Experiment C In the rst step current direction in each loop needs to be assumed It does not matter if we assume a wrong direction7 since the sign of the current in the solution to the Kirchho s Rules will tell us if we assumed the right direction negative solution indicates the opposite current direction Fig 1 shows one possible direction of currents that we adopt here There are two junctions in our circuit In general7 for N junctions it is enough to apply the junction rule to N 7 1 junctions Thus7 we need to write the rst rule only once hnn m V 2 DC CIRCUITS There are two loops in our circuit We need to apply the second rule to each of them Moving around the loops in the direction of the assumed current ow we have 1 R1 3 R3 7 61 0 loop on the left 2 2 R2 3 R3 7 62 0 loop on the right 3 For the potential difference across a resistor we have used Ohm7s law I 1 Assuming that the resistances and the potentials supplied by the batteries are known we need to solve the equations above for three currents 1 2 and 3 Since the number of equations equals the number of unknowns the problem can be solved By eliminating 3 putting 1 into 2 and we can reduce the problem to two equations with two unknowns 1 and 11R11112R3 61 4 2R2 11 2 R3 62 In the next step we can use the rst equation above to express 2 in terms of 1 and put this into the second equation This will leave us with one equation with one unknown 1 Solving it for 1 we get 6 E R3 17 27 11 P 21RB 5 Rmi Ri i Because of the symmetry of the circuit we can obtain formula for 2 by swapping indices 1 and 2 Finally 3 can be obtained from the sum of 1 and 2 B Exercises Please answer the questions on Report Sheet V71 which will be collected at the beginning of the laboratory session and graded by your instructor DC CIRCUITS V 3 v4 DC CIRCUITS REPORT SHEET V71 Date Name Instructor PRE LAB EXERCISES Exercise 1 Write junction rule for the junction shown below Exercise 2 Assume that in the circuit shown in Fig 1 all resistances are the sarne7 R1 R2 R3 R Express 1 in terms of 61 62 and B You can start from equation Show your algebra DC CIRCUITS V 5 blank V 6 DC CIRCUITS LABORATORY ASSIGNMENTS Experiment A Junction Rule The Task To experimentally verify Kirchhoff7s Junction Rule Materials Needed Resistors 10697 two 2209 Rheostat Power Supply Dual Channel Ampli er with two voltage probes ULl computer interface box 45V Battery for apparatus tests only Voltmeter for apparatus tests only 0 Cables Procedures Rheo stat J unctjgrg V V Figure 2 DC circuit used to verify Kirchhoffls Junction Rule DC CIRCUITS V 7 A1 The circuit used in this experiment is shown in Fig 2 Pattern of current ow in the junction will be varied by moving the slider of the rheostat which changes resistance of both circuit branches Ideally we should measure I7 I17 I2 and check if I I1 I2 6 Since we can measure only two currents at the same time7 we will measure currents leaving the junction I1 and I2 and we will keep the current entering the junction7 I7 constant Then7 it is enough to check that I1 I2 remains constant while I1 and I2 vary Instead of a battery we will use DC power supply which provides constant potential difference around 30V Changing position of the slider changes the effective resistance of the entire circuit7 thus changing I However7 10k 2 resistor in our circuit has resis tance much larger than any other element of the circuit7 thus dominating the effective resistance of entire circuit Therefore7 the effective resistance and the current I will be approximately constant To measure currents I1 and I2 we will measure potential drops over two 2209 resistors Il Vi220 Connect the circuit as shown in Fig 2 Connect 2209 resistors at the places indicated by the current meters A2 We will use two voltage probes in this experiment Make sure the probes are connected to the Dual Channel Ampli er and that the latter is connected to the UM interface box DlNl to DlNl7 DlN2 to DlN2 Switch the interface box on Start the computer7 and click on the PHY222 icon to start the program To load the proper initialization le7 choose Open from the File menu Open the le dc rule1 in PHY222 subdirectory Check the voltage probes using a test battery and hand held voltmeter A3 There are four graphs on your screen The top bottom left graph shows I1 I2 as a function of time The top right graph shows dependence of I1 on I2 Finally7 the bottom right plot shows dependence of the sum of the currents I1 I2 on time Switch the power supply on and set it to the maximal potential difference Make both I1 and I2 positive reverse the order in which the voltage probe leads are connected to the 2209 resistor if you need to change the sign Click on Collect and move the slider of the rheostat in its full range Copy I1 vs I2 and I1 I2 vs Time graphs onto Report Sheet V72 Did the junction rule work A4 Determine mean value of I1 I2 from your data click on I1 I2 vs Time graph7 V 8 Analyze menu a Statistics and compare it to the value of I expected from Ohm7s Law Report Sheet V72 To calculate the expected value of I assume that the effective resistance of the entire circuit is approximately 10k 2 since this is an underestimate for the total resistance7 we are likely to slightly overestimate I Make sure that you use the same units for I1 I2 and I in this comparison DC CIRCUITS REPORT SHEET V72 Date Name Instructor Partners A3 Current 1 vs Current 2 A3 1 2 A3 Currentl vs Time Time s DC CIRCUITS Are your I1 I2 vs Time data con sistent with Kirchhoff7s Junction Rule Explain A4 Expected value of I from Ohm7s Law I eR m Mean value of 112 Do these values roughly con rm the junction rule I I1 I2 v9 blank DC CIRCUITS Experiment B Loop Rule The Task To experimentally verify Kirchhoff7s Loop Rule Materials Needed Resistor 2209 Rheostat Dual Channel Ampli er with two voltage probes ULl computer interface box 45V Battery Cables Procedures Rheostat Figure 3 DC circuit used to verify Kirchhoffls Loop Rule B l The circuit used in this experiment is shown in Fig 3 There are three elements in this loop battery and two resistors rheostat plays a role of one of them Kirchhoff7s second rule written for this loop is V1 V2 7 6 0 7 where V1 is the potential difference across the rst resistor R1 22097 V2 is the potential difference across the second resistor ie rheostat R2 is variable and E is the potential difference generated by the battery 6 45V Since 6 is constant7 to DC CIRCUITS V 11 B2 prove the second rule we need to demonstrate that V1 V2 remains constant while V1 and V2 can vary individually Go to File77 menu and Open 77 to load dc rule277 set up le When the program asks you if you would like to save changes to the previous set up click on No Connect the circuit as shown in Fig 3 Make sure that one connection to the rheostat is to the slider Connect one voltage probe across 2209 resistor and the second one across the rheostat Make both voltage readings positive reverse the order of the voltage lead connections if necessary Click on Collect77 and move the slider of the rheostat in its full range Copy V1 vs V2 and V1 V2 vs Time graphs onto Report Sheet V73 Did the loop rule work B3 Determine mean value of V1 V2 from your data and compare it to the value of 6 measured for the battery Report Sheet V73 DC CIRCUITS REPORT SHEET V73 Date Name Instructor Partners B 2 Potential 1 vs Potential 2 132 Are your V1 V2 VS Time data consis tent with Kirchhost Loop Rule EX plain v2 v B3 B 2 Potentiall Potential2 VS Time potential difference generated by the battery Mean value of Do these values con rm the loop rule 6 V1 V27 Time s DC CIRCUITS V 13 blank DC CIRCUITS Experiment C Complex DC Circuit The Task To experimentally verify predictions based on the solution to Kirchhoffls Junction and Loop Rules Materials Needed Power Supply 45V Battery Voltage Divider Box Three 1009 Resistors Dual Channel Ampli er with two voltage probes ULl computer interface box Cables Procedures We will now study circuit which served as an example in the theoretical introduction Fig 1 We will use R1 R2 R3 R 10097 45V battery for 62 and the power supply as a source of variable 61 Using the formula 5 derived in the introduction we get 7261762 117 3B s 262761 I 7 9 2 3R ltgt 6 6 3Il12 To verify these equations we will measure dependence of the current in each branch on 61 C 1 Connect three 1009 resistors as shown in Fig 1 Connect 45V battery as 62 pay attention to the polarity Connect the power supply across the terminals A and B of the voltage divider box negative voltage to the terminal B Connect the terminals B and C of the voltage divider box as 61 in the circuit Pay attention to the polarity of the power supply connection the negative pole of the power supply black should be on the side of negative pole of the battery To measure 61 connect the voltage probe 1 across the terminals C and B of the box It is easy to make a mistake when wiring this circuit Make sure that the voltage probe is not connected directly to the power supply terminals A and B C 2 To verify formula 8 we will measure 1 by potential difference reading across the resistor R1 Connect the second voltage probe across this resistor 11 V21009 DC CIRCUITS V 15 c 03 Load the program set up which was previously used to study Ohm7s Law File77 menu a Open 77 a le ohms in PHY222 subdirectory With the power supply on and set to the maximum7 V1 and V2 or I E I1 should be both positive Switch the order of voltage probe lead connections to reverse the sign if needed Start collecting the data and vary 61 E V1 by turning the knob of the power supply from its minimal to its maximal setting you can also move back and fourth between the extreme settings The formula 8 predicts that the current I1 should be zero ie no current owing through the rst loop for 61 622 From your I vs V graph read out V for which the current is zero ls it half of the potential difference supplied by the battery see Report Sheet V74 C 4 We can further verify formula 8 by tting straight line to the Current vs Potential 3 5 data Select this graph by clicking on it Then go to Analyze77 menu and select Linear Fit From the box superimposed on the graph read the slope and the intercept of the tted line y mz b7 z 61 y I17 m slope b intercept From formula 8 slope should be E and intercept 73 Put into these formulae R 1009 and the battery voltage for 62 To compare to the tted slope and intercept multiply your theoretical predictions by 10007 since the current on your graph is displayed in units of mA rather than A Report the measured and predicted values in Report Sheet V74 Switch the voltage probe 2 to measure current I2 Collect data for varying 61 Fit a line to your I vs V graph Compare the tted slope and intercept to the expected ones from formula Report the measured and predicted values in Report Sheet V74 C 6 Switch the voltage probe 2 to measure current I3 Collect data to verify formula 10 DC CIRCUITS REPORT SHEET V74 Date Name Instructor Partners C 3 1 0 corresponds to 61 Half of battery voltage 622 Slope Intercept Expected Measured Expected Measured Formula Value Value Forrnula Value Value IDAV IDAV IDA IDA C 4 2 62 1 vs 61 7 C 5 2 vs 61 C 6 3 vs 61 DC CIRCUITS V 17 DC CIRCUITS
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