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Physics48 (Full201I)
Chupter26: Currentund Resistance
" Keep in mind that neither successnor failure is everfinal." - Roger Ward Babson
" Our greatestglory is not in neverfailing, but in rising up every)time we fail. "
Ralph Waldo Emerson
"If you continueto do what you've always done,you'll continueto get v,hatyou've alwaysgol."
Yogi Berra
" Defeat is not defeatunlessacceptedas a reality in your own mind. " - Btuce Lee
Reading: pages682 698
Outline:
3 electriccunent
definition
current
conventional
= currentdensity
drift speed
andresistivity
= resistance
variationswith temperatue
= Ohm'sLaw
= microscopicview of Ohm'sLaw (readon your own)
+ powerin electriccircuits
(readon your own)
andsuperconductors
= semiconductors
Problem Solving Techniques
You should know the definitions of cunent and current density,their relationshipto eachother, and
the relationshipbetweencunent density and drift velocity. Ifnet charge Aq passesthrough an areain
time At then the currentthrough the areais i = Aq/At. Ifarea A is perpendicularto the chargeflow
then the magnitudeofthe cunent density is J: i/A, where i is the current through the area.If
positive chargeis flowing the currentdensity is in the direction of its velocity; ifnegative chargeis
flowing the currentdensity is oppositeits velocity. The magnitudeofthe current density is relatedto
the drift speedv6 by J = nev6,where n is the number ofcharge carriers per unit volume in the
cunent.
You should know the definition of resistanceand be able to computethe resistanceR of a wire,
given its resistivity p, length L, and cross-sectionalareaA. The relationship 1, B = pLlA.
tiat resistivity is determinedto a largeextentby the meantime between
You shouldr.rnderstand
collisionsandthat this quantityis temperaturedependentbecausethe averagevelocity ofthe
electronsis temperaturedependent.The relationshipbetweenthe resistivity p andmeantime t
betweencollision is p = m/e2nr,wherem is the massof a chmgecarrierandn is the numberof
chargecarriersper unit volume in the current.
Chargecarrierslosekinetic energyin collisionswith the atomsof a resistor.You shouldknow how
to computethe rateof energydissipation,giventhe resistanceandeitherthe currentin the resistoror
the potential differencealongthe length ofthe resistor.use P = i2R or P = V2lR, wherei is the
currenlin the resistorandV is the potentialdifferenceacrossit.
Questionsand ExampleProblemsfrom Chapter 26
ProblemI
During the 4.0 min a 5.0 A cunent is setup in a wire, how many(a) coulombsand @) electronspass
throughany crosssectionacrossthe wire's width?
(".) t = a%/at -
4=5"oA
At = 4.o^"^^
= aqos
a7," u"oi
A b : CE.oft)(;.ros) =
]x losc
n = %/" = l.
(!) %=ne -?
t .t o ) . ' l 0
'c
----> n = ?.5' loar
Problem2
The magnitudeJ of the currentdensityin a certainwire with a circular crosssectionofradius
per squ e meterandradialdistancer
with J in amperes
R = 2.00mm is givenby J: (3.00x 108)12,
:
in meters.What is the currenttbroughthe outersectionboundedby r : 0.900Randr R?
; = !J.rR
\--l
$=(:'oo:1orV.') JA= 0'n.dr
5=Br'
RR
co-to'= An B ( atJ.
i" = <(
\ - -Bc")1ancJ.)
l\
/
)
'
= -L:E
rl
/
/
o'9oo8
o'i66
- ^.r -n(3.oo^ro?*A:]La-pdollcs"qe
7^
'/ J---=--T!08
f
l_[o"qo..,rrJ'^
Problem3
=
A fusein an electriccircuit is a wire that is designedto melt, andtherebyopenthe circuit, if the piQlAl
currentexceedsa predeterminedvalue. Supposethat the materialto be usedin a fusemelts whenthgr-currentdensityrisis to 440 A,/cm2.What diameterof cylindrical wire shouldbe usedto makea fuse
that will limit the currentto 0.50A?
- TB/^
t' =
L
-r-''*'t)
[ Rq/o.9oo1)11 -=
J
-Ln
=
4'lo"l)' hfn^
[ = o.soq
= i/A = i/rc^
T
(ffj.
{= 4tov.,.,*
\-
+3
f-= J.q^lo1r.,
,61:"a'"ot, = 3r
=
Problem 4
A small but measurablecurrent of 1.2 x 10-10A exists in a copper wire whose diameteris 2.5 mm.
The number of chargecarriersper unit volume is 8.48 x 1028m-3.Assuming the current is uniform,
calculatethe (a) current density and (b) electron drift speed.
''A
;-- 1'1x 1o
=
a = | , 4 5 m r . ,t . a 5 ^l d ' -
/\ -a\
'l
: !.rexlo".nu
p1
5= i/n,') =
t/a
"r-=
J - /
f=?
.,,$c".^ru^JttAl",&.,,r-,
:F,#"lo--E
#:#.
\-:--------:-1
Problems
lVa=
l'8o'.lo-'-r"' I
(a nickel--chromium-iron
alioy commonlyusedin heatingelements)is 1.0m
A wire of Nicbro^me
area.It carriesa currentof 4.0 A whena 2.0 V potential
longand 1.0mm' in cross-sectional
differenceis appliedbetweenits ends.Calcuiatethe conductivityo ofNichrome.
/ = l.o*
ft = l.o -'3
=
Lo * lo-"".ru
t = 4-oA
V = e-ov
A=QL/a
l
n=v/;
6-=
Y/r'QLA=
)
/P= CL
AV
(=ry
( t . o xt c b " , r ){ ? . o v )
6 = I,o*-lo"JL-n-,
Problem6
A commonflashlightbulb is ratedat 0.30A and2.9 V (thevaluesof the currentandvoltageunder
(20'C) is 1.1O,
operatingconditions).If the resistance
of the bulb filamentat room temperature
what is the temperatureof the filament whenthe bulb is on?The filament is madeof tunssten.
-
o
lolJl-
1.r>funa1 --:
B=Y; -
a .9V -- 1.t",1sto.jh
F-.Arfu\ -t = ?"5 x lo=./c"
A- B"=R "* (-r-r.)
T-t --
xB"
B-4
T=
To.
A- A"
4"a'
-l-=
? . o " C+ ( i . r , " r r - 1 . t n )
(r,ro-)(+-s^lt%,
l-= l?5t"c
Problem7
An unknownresistoris connectedbetweenthe terminalsofa 3.00 V battery.Energyis dissipatedin
the resistorat the rate of 0.540W. The sameresistoris then connectedbetweentle terminalsof a
1.50V battery.At what rate is enerry now dissipated?
.\,r
!=
?=;'B="7n--' A'+
3'ooV
P - o"5qaw
D.59ovV
B = ib"?-l
P= ? ,rqrr "/= t'soV ..-,
?, u7r.=
O. )35 \^/
Problem8
A 1250W radiantheateris constuctedto operateat 115V. (a) What will be the currentin the
heater?(b) What is the resistanceof the heatingcoil? (c) How mubhthermalenergyis producedin
1.0 h by the heater?
(") f =;V---,t =?/v- 'j3y =ltoTA]
P= l?'5otn/
v=lr5v
(b)
.c,a/e,u^{A=Y/;
A=
(.) P = JtAt
=E/t?
*t*
-. +^1*n
P-v/n -- h =uh
-1f'"'q
A = uti,:
=llD.b-n- /
l?.5ow
E =?t = ( t>sow)(aaoo.;
E=
4.5x lo 55
Problem9
A 100W light bulb is pluggedinto a standard120V oullet.(a) How muchdoesit costper 3l-day
month to leavethe light tumed on continuously?Assumeelectricenergycosts6llkW'h. (b) What is
the resistaaceof the bulb? (c) What is the cunent in the bulb?
)
,,^* ^t"d l" &"r!-t -"J-tr-",
^-.-,,,g KW.h -|nar looWru.vnnvng 8q3l)^Xa
( roow)(!N*.*) (.l",.r,) (at*./;*nS = ?c.1 K\i h
"
(4J
6nrt = (?t.qKw"h)( 6%r.n.) = 4I(o.,iu =Fitlq
( b)
?=Y/r
(.)
? = tV
g=Y/p = t,rou{oo, =7*;1
)
-) t=w=
iaov
lOoW
n ?ae a