Experiment 23
Experiment Experiment 23: Wheatstone Bridge Br idge and Resistivity of Metals Purpose (1) To study the use of Wheatstone Wheatstone Bridge for precise measureme measurements nts of resistances. resistances. (2) To determine determine the resistiv resistivity ity of a metal.
Apparatus (a) a slide slide wire, a galvanometer with a protector, a decade resistance resistance bo (b) an ammeter, a !" power supply, wire samples, electrical connectors
Theory #) $esistance of a Wire. Wire. The resistance of a wire can be calculated calculated from %&uation (1) (1 ) where' length of the wire. * cross sectional area of the wire. + resistivity of the metal of the wire.
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L A
##) Wheatstone Bridge. This is a device for the precise measurements of resistances. #t is based on the diagram in -ig. -ig. 1. *t point *, an incomi incoming ng current splits splits into two currents, # and #1. #n general, there is a crossover current between points " and !, which can be detected detec ted by the galvanometer. owever, oweve r, if the resistances $ 1 and $ 2 are properly chosen, the crossover current will be ero (as the galvanometer will show). This happens when the four resistances in -ig. 1 satisfy %&uation %&uat ion (2). This is 3nown as the Balanced Bridge 4osition. B**5"%! B$#!6% B*#" %70*T#5
(2)
$ 8
$ 1
$ 9
$ 2
#n this eperiment, the resistances $ 1 and $ 2 stem from two lengths of a uniform wire made of one metal metal with a constant constant cross section. -rom e&uation (1), we 3now that that the ratio $ 1: $ 2 is the same as the ratio 1: 2 of their lengths. #f $ 9 is 3nown, the 118
Experiment 23
un3nown resistance can be found from (2).
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Experiment 23
Proedure a) n your data sheet, record the code number of your set of samples. $ecord the following data on all of the wires' the lengths, the gauge, and the type of metal. !" #"T $%&P T'&$ $TEP( 4repare the following table'
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T*B% 5%' /%*0$%/%5T : $%#T*5"% $05 $ 9 1 2 $ 8 *verage' < $ 8 = ; 1 2 ? 1 2 ?
((((( (etc.)
b) %ngage Wire 5o. > as $ and set $ 9 29 ohms. c) *ssemble the entire circuit according to -ig. 2. /a3e sure you understand why the points mar3ed by same letters (*, B, ", !) are at the same electrical potential.
d) /a3e sure that all connection screws are tight and that all connectors fit tightly in their soc3ets. ! 5T 4$"%%! 05T# A0$ #5T$0"T$ * *44$%! A0$ "#$"0#T. e) 4lug in the power supply and turn on the power. et the current to about 2>9 ma. 120
Experiment 23
Aou do not have to adCust it again. et the tap 3ey near the middle of the slide wire and press it. Aou should see a small deflection of the galvanometer needle. #f it is very large, or if there is no deflection, chec3 with the instructor. f) lide the tap 3ey bac3 and forth until you find a position where the galvanometer shows no noticeable deflection. This position is *44$8#/*T%A the balanced bridge position. g) 5ow press the protector button. This increases the sensitivity of the galvanometer so that you can find the balanced bridge position precisely when you pressing and moving the tap 3ey slightly. Deep the protector button depressed, and locate the balanced bridge position to 9.1 centimeter precision. $ecord the values of $ 9 and 1 , and 2 199.9 cm E 1 for Wire 5o. >, $un ;1. h) $epeat (f) and (g) for $ 9 1F ohms and $ 9 12 ohms, still using Wire 5o. >. $ecord $ 9 , 1 , and 2 for $uns ;2 and ;?. i) /a3e three runs for each wire. 0se these suggested values of $ 9' $ecord the values of $ 9 , 1 , and 2 for each run.
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066%T%! $ 9 (ohms) F, 1, @, ?,
>, 2, ?, 2,
B%-$% A0 %*% T% *B' Turn off the power in your power supply, and unplug it. !isconnect everything in your circuit and return all connectors to their proper places.
)a* Report Part &( 1) "alculate the value of $ for each of your samples and record it on Table ne in the $ column. -ind the average value <$ = for each sample.
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@ ? 2 1
Experiment 23
2) "opy Table Two onto your report. -ill it in and calculate resistivities for each sample. using %&uation (1). (5ote that the diameters of wires are indicated by their gauges' gauge 22 means ! 9.F?>mmG gauge 2H means ! 9.?9> mm.)
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< $ =
+
?) "alculate the resistivity of copper as the average <+= of all your opper samples. "ompare with the correct value of 1.I2 19EH ohmEmeter and display your J discrepancy. Be careful with units. @) *nswer the following &uestions' 7uestion 1. #s it possible that, during your eperiment, the resistance of one of your wires has changedK #f yes, what is the li3ely reasonK What precautions should be ta3en to guard against thisK
7uestion 2' #n this eperiment, there is an uncertainty of 9.1cm in locating the Balanced Bridge 4osition.What J error will this uncertainty cause in calculations of 1 , of 2 , and of the ratio 1 : 2 , when 1 happens to be (a) 29.9 cm (b) L9.9cm (c) >9.9 cmK how the details of your calculations and display the results in the table .
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2
1 29 cm 1 L9 cm
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1 >9 cm
7uestion ?' n the basis of the above table for 7uestion 2, eplain the reasons for the suggested values of R + in M4rocedureN.
0se calculus methods to answer this &uestion (i.e. use differentials to estimate small errors O uncertainties) if you can.
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