General Physics Laboratory II
General Physics Laboratory II PHY 222
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This 20 page Class Notes was uploaded by Clement Bernier 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 16 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
IV OHM S LAW f0501 INTRODUCTION The electric eld with which you are familiar from the previous experiments usually causes a ow of charges or simply an electric current Ohm7s Law says that a value of electric current in a piece of conductor depends linearly on the electric potential applied to it I E The constant B is called electrical resistance and it depends on the material forming the conductive element its size and shape but it does not depend on the applied potential Unlike fundamental Coulomb7s and Gauss7 Laws which are always true Ohm7s Law is not universally true For example for semi conducting elements like diodes Ohm7s Law is not obeyed at all Elements which obey Ohm7s Law are called resistors Different resistors can be combined into a circuit The ow of current through each element of the circuit is completely charac terized by the total applied voltage and the resistance of the individual resistors We will learn the rules for calculating the effective resistance of a composite circuit PURPOSE 0 Study of elements that obey and violate Ohm7s Law 0 Veri cation of the rules for resistors arranged in parallel or in series OHM S LAW lV l PRE LAB ASSIGNMENTS A Readings Ohm7s Law states that the current I through a piece of conductor depends linearly on the potential difference V between the two ends of the conductor For objects that obey Ohm7s Law we may de ne a constant quantity electrical resistance R which is simply the ratio of the potential difference and the current V R i 1 I lt gt We measure resistance in units of Q E Ohm VoltlAmpere For elements that dont obey Ohm7s Law the resistance is not a constant quantity7 thus it does not play a useful rule Elements which obey Ohm7s Law are called resistors What happens if we combine two such resistors together in series R2 The current through them has to be the same7 even if the resistors are different7 because the current cannot be lost along its path The total voltage drop across the two resistors will be the sum of the voltage drops across each of them V 1 211R112R2IR1R2 From 1 V Raff therefore7 we have the series rule for the effective resistance Raff Raff R1 R27 2 which can be easily generalized to an arbitrary number of resistors RaffR1R2R3R4 3 lV 2 OHM S LAW This rule sirnply says that n resistors connected in series are equivalent to a single resistor with the resistance Raff If we connect resistors in parallel with the battery R1 R2 lt then the voltage drop across them will be the same and equal to the voltage of the battery while the total current will be the sum of the two currents owing through each of them I 11 2 VR1 VR2 V1R1 1R2 VReff Therefore we have the parallel rule 1Reff1R11R21R3 4 for the effective resistance ofthe circuit consisting of the resistances R1 R2 R3 connected in parallel For example for two identical resistors with resistance R connected in parallel we have Raff R2 check itl which makes sense because the current has twice as many ways to ow You can think of two resistors in parallel as a two lane highway which allows twice as many cars to ow during heavy traf c as would a single lane road Circuits can be more complicated than resistors connected just in series or in parallel However it is often possible to think of a circuit as consisting of a few blocks each being like a single effective resistor connected in parallel or in series to the rest Each block can be in turn separated into a few sub blocks and so on until we break each sub block down to a single resistor OHM S LAW lV 3 For instance the circuit consisting of resistors connected like this Re is equivalent to two effective resistors R0 and RP connected in series Re where according to formula 4 R1 R2 R1 R2 1Rp 1R1 1132 so RP R1 R2 therefore Raff R0 B Exercises Please answer the questions on Report Sheet lV71 which will be collected at the beginning of the laboratory session and graded by your instructor lV 4 OHM S LAW REPORT SHEET IVil Date Name Instructor PRE LAB EXERCISES Exercise 1 At horne7 if you plug two lamps in the same dlouble outlet7 are you connecting these lamps in series or in parallel Explain Exercise 2 Assume you have two 1009 resistors7 but need 509 resistor ls there a way to connect the 1009 resistors to get 5097 Exercise 3 Calculate effective resistance of three resistors connected as shown RFIOOQ 113509 OHM S LAW lV 5 blank OHM S LAW LABORATORY ASSIGNMENTS Materials Needed 0 Resistors 29 22097 two 1009 o Diode Experiment B o Rheostat 0 45V Battery 0 Dual Channel Ampli er with voltage probes o ULl computer interface box 0 Voltmeter for apparatus test only 0 Cables Experiment A Ohm s Law The Task To observe linear dependence of I on V for a resistor and to measure its resistance7 R Procedures Al To verify Ohm7s Law we need to measure the potential difference V across the resistor and the current I owing through it for a wide range of V The circuit to perform these measurements is shown here M 4 To vary V we need to use variable source of potential difference This can be achieved by connecting a battery to a rheostat as shown in gure below Rheostat is a device OHM S LAW lV 7 with which resistance can be varied We will use a rheostat in which the resistance is controlled by a slider on top of the resistive cylinder Although the battery will supply a constant potential difference of 45 Volts7 whatever is connected to our battery rheostat unit will receive the potential difference of E 45 ilRrheosmt I is the current owing through the rheostat Change of Rrheosm will irnply change of 6 mil 45V Rheostat To measure the potential difference across the resistor7 we will use the computer ized voltage probe with the two leads connected to the two ends of the resistor 8 Most of devices that measure current 0 ernploy Ohrn7s Law and simply measure the potential difference V across the known resistor as shown below We will use 1009 resistor7 thus I V 1OOQ You may be disturbed that we are using Ohrn7s Law here7 even though the experiment itself is designed to verify Ohrn7s Law validity Dont worry There is no logical inconsistency If the experiment shows that Ohrn7s Law works7 we were right to employ it to measure the current If the experiment fails to con rm Ohrn7s Law7 we will conclude that the law failed either across the resistor under study or across the resistor used in the current measurement IV 100 2 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 cornputer7 and click on the PHY222 icon to start the program To load the proper initialization le7 choose Open 77 from the File77 menu Open the le ohrns in PHY222 subdirectory OHM S LAW OHM S LAW 03 a In the rst step you must check calibration of the voltage probes The voltage read from probe 1 2 is displayed as V1 V2 below the graph area They should read zero when directly connecting the red and black leads to each other Measure voltage of a test battery with a hand held voltmeter Then connect the same battery to the voltage probe the black lead to the pole of the battery7 the red lead to the pole and see if the computer reads a similar value Notify the instructor if the computer does not read reasonable voltage values Connect one pole of the battery to the slider on the rheostat there is a terminal at the end of the metal bar on which the slider moves Connect 2209 resistor to the other pole of the battery Connect the other end of this resistor to 1009 resistor which will be used for the current measurement Finally connect the other end of the 1009 resistor to one of the bottom terminals of the rheostat Connect the voltage probe 1 across the 2209 resistor V1 in the computer will be V from Fig 1 and the voltage probe 2 across the 1009 resistor The latter voltage will be converted by the computer to the value of current I Order of connecting blackred leads of the voltage probes matters and changes sign of the measured values Connect the leads in a way that both V1 and V2 or I are positive Click on the Collect button The computer will collect data for 10seconds Vary the supplied potential by smoothly moving the slider on the rheostat Make sure that you reach both extreme positions of the slider on each end of the rheostat You can move back and fourth between the two ends There are four graphs on your screen The top left graph shows the voltage difference V V1 across the studied 2209 resistor as a function of time The bottom left graph shows the current I I V21OOQ owing in our circuit as a function of time The top right graph shows dependence of I on V Finally7 the bottom right plot shows how the ratio VI changes with time Copy the I vs V graph onto Report Sheet lV72 ls it linear as expected from Ohm7s Law The other way to see if Ohm7s Law works is to look at the dependence of VI on time Since this ratio is simply the resistance of the resistor7 it should be constant Any deviations from atness are due to the measurement inaccuracies Actual resistance of the resistor may be somewhat different from its nominal rating We can determine the actual resistance from our data For the best measurement of the resistance average the data from the VI vs Time graph by selecting it click on it and then going to Analyze menu and nally choosing Statistics This should superimpose a box on your graph in which you can nd the mean ie average value Copy it to Report Sheet lV72 How far is your measurement from the nominal value of the resistor Repeat the measurement for the second 1009 resistor connected instead of the 2209 resistor Determine average value of R and also copy it to Report Sheet lV72 A5 Now try to measure actual resistance of 29 resistor You are likely to run into problems with the method we have been using so far7 since the potential difference across the resistor is so small that it becomes comparable to the measurement inaccuracies and we cannot measure it very well One possible solution is to move the slider on the rheostat only at the end that produces the highest potential difference and current across the resistor Even better way is to perform a t of a straight line to the I vs V graph Select this graph by clicking on it Go to Analyze77 menu and select Linear Fit This should superimpose the tted line on your graph and a box with the t results The tted functions is y mz b77 where in our case y I7 z V and the slope m 1R Thus7 you can determine resistance by inverting m Since we graph the current in units of milliampers 771A7 to obtain resistance in units of Ohms you should calculate R 1000m lV 10 OHM S LAW REPORT SHEET IV72 Date Name Instructor Partners A Current vs Potential for 2209 resistor V V Nominal resistance Measured resistance A 3 2209 A 4 1009 A 5 29 OHM S LAW IV ll blank IV 12 OHM S LAW Experiment B Diode The Task To illustrate that not all electric elements follow Ohm7s Law Procedures B l Connect a diode instead of the resistor into our measurement circuit Make the diode arrow point to the negative pole of the battery Collect the data and copy I vs V graph and VI vs time graph onto Report Sheet lV73 Do not forget to indicate range of observed values on the I7 V and VI axes Change the direction in which the diode is connected to the circuit the diode arrow pointing to the positive pole of the battery Collect the data Dont be alarmed if the data look like a mess Note down in Report Sheet lV73 the maximal absolute value of the current through the diode you have obtained Compare it to the maximal value of the current you have achieved with the diode connected the other way ie in B l 93 D OHM S LAW lV 13 IV 14 OHM S LAW REPORT SHEET IV73 Date lnstructor Partners B l Current vs Potential B l V V B l Resistance vs Time V1 9 Time s OHM S LAW Does the diode ful ll Ohm7s Law EX plain Does the diode have a constant resis tance B 2 Maximal absolute value of current for the reverse connections of the diode lIlmam What can you say about value of the current through the diode in this case as compared to the maximal value ob tained in B l lV 15 blank IV 16 OHM S LAW Experiment CF Resistors Connected in Series and in Parallel The Task To verify the rules for effective resistance of resistors connected in series and in parallel Procedures If for any of con gurations of resitors you are going to study7 the effective resistance becomes small7 use the t method described in A 5 rather than averaging of the VI mea surements C OHM S LAW Connect in series 2209 and 1009 resistors instead of the diode The voltage probe 1 should be connected across both resistors Collect the data for varying applied poten tial From VI vs time graph calculate average effective resitance and note it down in Report Sheet lV74 Calculate the expected effective resitance from the rule for the resistors connected in series Use the measured rather than nominal values of the re sitance for each resistor from lV72 Report your calculation in Report Sheet lV74 How does the measured effective resistance compare with the calculated one Now connect the same resitors in parallel Collect the data for varying applied potential and determine average effective resitance Calculate the expected effective resistance and report both in Report Sheet lV74 Add 29 resistor in parallel to the other resistors Before making any measurements or calculations make a rough guess of the effective resistance of the three resistors connected in parallel Now make the measurement and the calculation Report Sheet 1V4 Connect 29 resistor in series with 2209 and 1009 resistors connected in parallel Make a rough guess of the effective resistance of the system of resistors Now make the measurement and the calculation Report Sheet lV74 lV 17 IV 18 OHM S LAW REPORT SHEET IV74 Date Name Instructor Partners Effective Resistance Experiment Measured Expected Value Formula Value R ZZZUQ RflUELQ C Ram Rzznu g RFZZELQ Ran OHM S LAW IV 19 IV 20 OHM S LAW
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