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WHEATSTONE WHEATSTONE BRIDGE
LAB REPORT PHY 204 OCTOBER 6, 2011
Introduction A Wheatstone bride is an e!e"tri"a! "ir"#it #sed to $eas#re an #n%no&n e!e"tri"a! resistan"e b' resistan"e b' ba!an"in t&o !es o( a bride a bride "ir"#it, "ir"#it, one !e o( &hi"h in"!#des the
-2#n%no&n "o$)onent* +t &as inented b' a$#e! H#nter Christie in 1.// and i$)roed and )o)#!aried b' ir Char!es Wheatstone in 1.4/* The adantae o( this dei"e is that it e!i$inates the interna! resistan"e or "#rrent that other $eas#re$ent dei"es hae, &hi"h e((e"t the "ir"#it the' are $eas#rin* This is )ossib!e be"a#se &hen the t&o !es o( the "ir"#it are ba!an"ed there is no "#rrent (!o&in bet&een the$, &hi"h n ot on!' te!!s 'o# that the "ir"#it is ba!an"ed b#t &hen the "#rrent is ero, there is no e((e"t o( the $eter on the "ir"#it* When this !ab is "o$)!ete, a st#dent &i!! hae a better #nderstandin o( "ir"#it testin dei"es, es)e"ia!!' the oh$$eter, their #ses, adantaes and disadantaes, and s)e"i(i"a!!' ho& to "onstr#"t a Wheatstone bride to $a%e the $ore a""#rate resistan"e $eas#re$ents*
Apparatus o o o o o o o o o o
Wheatstone bride board Resistan"e Bo &ith ad#stab!e resistan"e a!#es 23 )o&er s#))!' a!ano$eter Rheostat 1 $eter o( 5iChro$e Wire *010 7eter sti"% 7i"ro$eter 8iita! 7#!ti$eter in!e "!a' resistor in the 9: Oh$ rane
Procedure Part I. Conne"t the "ir"#it as sho&n in ;i#re 2* et the resistan"e bo R1 to < oh$s* C#t 1 $eter o( &ire (ro$ the s)oo! and "onne"t one end to the s"re& in the "enter o( the Bride board and the other to the a!!iator "!i) (ro$ the a!ano$eter at a distan"e o( 90 C$ (ro$ the s"re&* The rheostat "an be #sed to ad#st the sensitiit' o( the bride, =b#t in o#r "ase the rheostat &as not $a%in a "onne"tion an'&here e"e)t (or the !o&est settin )osition so it "o#!d not be )ro)er!' #sed*> Ta%e the other end o( the a!ano $eter and "onne"t it near the "enter o( the L1?!2 &ire* Obsere the need!e o( the a!ano$eter as the "!i) is $oed a!on the
-/L1?L2 &ire and (ind a )!a"e &here the need!e reads ero* This )oint deter$ines L1 be"o$es L2* Re"ord the distan"es o( L1 and L2* Re)eat these $eas#re$ents (or &ire !enths o( 60, <0, .0, @0, and 100 C$* Part II. Ta%e the resistor )roided b' the TA and read and re"ord the "o!or "ode* et the
resistan"e bo to a a!#e that is a))roi$ate!' &ithin 20 o( the resistor a!#e* se a 877 set to oh$s, $eas#re and re"ord another readin o( the resistan"e a!#e* C!i) the resistor in )!a"e o( the &ire in the )reio#s e)eri$ent and #se the sa$e )ro"ess as the )reio#s e)eri$ent to "a!"#!ate the resistor a!#e* Re"ord resistor a!#e so 'o# en d #) #sin three di((erent $eas#re$ent $ethods to (ind the resistan"e*
Data Book
Experiment I -- Resistance Calculations Material = Ø0.0254 (CM) NiCrome !en"t o# $ire (M)
R% &alue ('ms)
!% (M)
!2 (M)
R ('ms)
0.45
7
0.58
0.42
9.67
0.55
7
0.63
0.37
11.92
0.65
7
0.67
0.33
14.21
0.75
7
0.7
0.3
16.33
0.85
7
0.72
0.28
18.00
0.95
7
0.75
0.25
21.00
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Experiment I -- Resisti&it* Calculations Material = Ø0.0254 (CM) NiCrome +lope #rom Experiment % ,rap
Raius o# $ire (M)
rea (M2 )
Resisti&it * ('m /M)
22.009
1.27E-04
5.067E-08
1.12E-06
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Experiment II ri"e Calculation 1nno$n Resistor
R% &alue ('ms)
!% (CM)
!2 (CM)
R ('ms)
RX
5100
50.5
49.5
5203.03
Experiment II Results 1nno$n Resistor 1nno$n Resistor
ri"e 3alue ('ms)
Color coe 3alue ('ms)
'mmeter 3alue
RX
5203
5100
5180
Analysis The idea in this !ab is that $eas#rin the resistan"e in the Wheatstone bride $ethod ie a $ore a""#rate readin be"a#se the interna! resistan"e o( the $eters are ta%en o#t o( the e#ation* the !oner the L1?L2 are the $ore reso!#tion and !ess error the set#) sho#!d hae* in"e the readin o( &hen the a!ano$eter sho&s a ba!an"ed "ir"#it is ero, this !o&ers the "o$)!eit' o( the $eter sin"e it "an $eas#re ero "#rrent re!atie!' a""#rate!'* alculations The "a!"#!ations is this !ab &ere #ite straiht (or&ard* A"t#a!!' + !et E"e! do a!!
the &or%* To "a!"#!ate the resistan"es o( the !enths o( ni"hro$e &ire, the "a!"#!ation is si$)!e the ratio o( L1 ?L2 $#!ti)!ied b' R1To "a!"#!ate the resistiit' &e need the s!o)e o( o#r ra)h,
-6&hi"h is #st the resistan"e diided b' the !enth* This is $#!ti)!ied b' the area &hi"h o( "o#rse is )iDR2 Si!ni"icant #i!ures + did not at a!! (ee! "on(ident &ith the e#i)$ent #sed in the !ab* + did not
hae an' $ethod o( "a!ibratin o#r res#!ts aainst a )ositie!' %no&n res#!t and &e did not %no& the a"t#a! error in the resistor de"ade bo or the sin!e "!a' resistor so +F$ "on"!#din an error rane o( #) to 20
Discussion One )oint that + (e!t &as sini(i"ant in this !ab is the idea that #sin so$e basi" e#ation $ani)#!ation "o$bined &ith so$e basi" hard&are, a ne& dei"e "an be $ade that reat!' i$)roes the a""#ra"' o( the $eas#rin e#i)$ent* This !esson sho#!d be re$e$bered and a))!ied to (#t#re )h'si"s )rob!e$s or sit#ations* + s#s)e"t that there $a' be so$e hidden resistan"e in the hard&are o( the bride e#i)$ent* +t &as er' o!d and to "o$)!ete the set#), $an' &ire !eads had to be "onne"ted* +( the n#$ber o( sha%' "onne"tions "o#!d be e!i$inated, + &o#!d e)e"t the a""#ra"' &o#!d o #)* + &o#!d !i%e a resistor o( a )ositie!' %no& a!#e to be aai!ab!e* This &a' a test "o#!d be $ade o( the a""#ra"' and boost "on(iden"e in the a""#ra"' o( the )ro"ess*
onclusion +n this !ab &e hae s#""ess(#!!' #sed the bride dei"e to $eas#re resistan"e* in"e &e $eas#red a %no&n resistor and had a readin &ithin the to!eran"e rane o( the resistor &e "an "on"!#de that o#r $eas#re$ents are at !east "!ose to bein "orre"t* Ho&eer, &itho#t hain an' %no&!ede o( the a"t#a! a!#e o( the resistan"e o( the ni"hro$e &ire it &o#!d be )re$at#re to "on"!#de that o#t tests are $ore a""#rate then the 877 $eas#re$ents
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Analysis $uestions 1*
Is t%ere a di""erence &et'een t%e resistor color code and t%e &rid!e (alue) Yes* The
resistor "o!or "ode o( reen Bro&n Red o!d indi"ate a no$ina! resistan"e o( 9100 oh$s &ith a to!eran"e o( 9 &hi!e the bride $eas#red 920/* The G9 on the to!eran"e a!!o&s a rane or 4.49 to9/99 oh$s &hi"h "o#!d e)!ain the di((eren"e* This ass#$es that o#r bride &as a"t#a!!' $eas#rin "orre"t!'*
