Chapter  17Current  and  Resistance

1. Three charged particles are arranged on corners of a square as shown in Figure

MC

Q15.12, w

ith charge -Q on both the particle at the

upper left corner and the particle at the lower right

corner, and charge +2Q on the particle at the low

er leftright corner. W

hat is the direction of the electric field at the upper right corner w

hich is a point in empty space? (a) upw

ard and to theright (b) to the right (c) dow

nward (d) dow

nward and

to the left (e) The field is exactly zero at that point.

2. If more electric field lines leave a G

aussian surface than enter it, what can you

conclude about the net charge enclosed by that surface?

3. Why is it im

portant to avoid sharp edges or points on conductors used in high-voltage equipm

ent?

4. Rank the potential energies of the four system

s of particlesshow

n in Figure from largest to sm

allest.Include equalities if appropriate.

Quiz 3

(Must show

work to get full credit)

1. If three unequal capacitors, initially uncharged, areconnected in series across a battery, w

hich of thefollow

ing statements is true? (a) The equivalent

capacitance is greater than any of the individualcapacitances.(b) The largest voltage appears across thecapacitor w

ith the smallest capacitance. (c) The largest

voltage appears across the capacitor with the largest

capacitance. (d) The capacitor with the largest

capacitance has the greatest charge. (e) The capacitorw

ith the smallest capacitance has the sm

allest charge.

2. Consider positive and negative charges m

oving horizontally through the four regions in Figure. Rank  themagnitudes  of  the  currents  in  these  four  regions  from

 low

est  to  highest.

Current

•Prac<cal  applica<ons  were  based  on  sta<c

electricity.•A  steady  source  of  electric  current  allow

edscien<sts  to  learn  how

 to  control  the  flow  of

electric  charges  in  circuits.

Introduc<on

Electric  Current

•The  current  is  the  rate  at  which  the  charge  flow

sthrough  a  surface.–Look  at  the  charges  flow

ing  perpendicularly  through  a  surfaceof  area  A

.–•The  SI  unit  of  current  is  A

mpere  (A

)–1  A

 =  1  C/s

Sec<on  17.1

Instantaneous  Current

•The  instantaneous  current  is  the  limit  of  the  average

current  as  the  <me  interval  goes  to  zero:

•••If  there  is  a  steady  current,  the  average  andinstantaneous  currents  w

ill  be  the  same.

•SI  unit:  A•

Sec<on  17.1

Electric  Current,  Cont.•The  direc<on  of  the  current  is  thedirec<on  posi<ve  charge  w

ould  flow.

–This  is  known  as  conven&onal  current

direc&on.•In  a  com

mon  conductor,  such  as  copper,  the

current  is  due  to  the  mo<on  of  the  nega<vely

charged  electrons.

•It  is  common  to  refer  to  a  m

ovingcharge  as  a  m

obile  charge  carrier.–A

 charge  carrier  can  be  posi<ve  ornega<ve.

Sec<on  17.1

Power

•In  a  conductor  carrying  a  current,  the  electricpoten<al  of  the  charges  is  con<nuallydecreasing.•Posi<ve  charges  m

ove  from  regions  of  high

poten<al  to  regions  of  low  poten<al.

• ΔUcharges  =  q  ΔV  is  nega<ve

–OSen  only  the  m

agnitude  is  desired•The  pow

er  delivered  to  the  circuit  element  is

the  energy  divided  by  the  elapsed  <me.

Sec<on  17.1

Current  and  DriS

 Speed

•Charged  par<cles  move

through  a  conductor  of  cross-­‐sec<onal  area  A

.•n  is  the  num

ber  of  chargecarriers  per  unit  volum

e.•n  A

 Δx  is  the  total  number  of

charge  carriers.

Sec<on  17.2

Current  and  DriS

 Speed,  Cont.

•The  total  charge  is  the  number  of  carriers  <m

es  thecharge  per  carrier,  q–ΔQ

 =  (n  A  Δx)  q

• The  driS  speed,  v

d ,  is  the  speed  at  which  the  carriers

move.

– vd  =  Δx/  Δt

• RewriY

en:  ΔQ  =  (n  A

 vd  Δt)  q

• Finally,  current,  I  =  ΔQ/Δt  =  nqv

d A

•Sec<on  17.2

Current  and  DriS

 Speed,  Final

•If  the  conductor  is  isolated,  the  electronsundergo  random

 mo<on.

•When  an  electric  field  is  set  up  in  the

conductor,  it  creates  an  electric  force  on  theelectrons  and  hence  a  current.

Sec<on  17.2

Charge  Carrier  Mo<on  in  a  Conductor

•The  zig-­‐zag  black  linerepresents  the  m

o<on  of  acharge  carrier  in  a  conductor.–The  net  driS

 speed  is  small.

•The  sharp  changes  indirec<on  are  due  to  collisions.•The  net  m

o<on  of  electrons  isopposite  the  direc<on  of  theelectric  field.

Sec<on  17.2

Electrons  in  a  Circuit

•Assum

e  you  close  a  switch  to  turn  on  a  light.

•The  electrons  do  not  travel  from  the  sw

itch  to  thebulb.•The  electrons  already  in  the  bulb  m

ove  in  response  tothe  electric  field  set  up  in  the  com

pleted  circuit.•A  baY

ery  in  a  circuit  supplies  energy  (not  charges)  tothe  circuit.

The amount of charge that passes through the

filament of a certain lightbulb in 2.00 s is 1.67 C

.Find (a

)the average current in the lightbulb and(b

)the number of electrons that pass through

the filament in 5.00 s. (c

)If the current issupplied by a 12.0-V battery, w

hat total energy isdelivered to the lightbulb filam

ent? What is the

average power?

Electrons  in  a  Circuit,  Cont.

•The  driS  speed  is  m

uch  smaller  than  the  average

speed  between  collisions.

•When  a  circuit  is  com

pleted,  the  electric  field  travelswith  a  speed  close  to  the  speed  of  light.•Although  the  driS

 speed  is  on  the  order  of  10-­‐4  m

/s,the  eff

ect  of  the  electric  field  is  felt  on  the  order  of  108  

m/s.

Sec<on  17.2

A copper wire of cross-sectional area 3.00x10

-26 m

2 carries a current of 10.0 A. (a)Assum

ingeach copper atom

contributes one free electronto the m

etal, find the drift speed of the electronsin this w

ire. (b)U

se the ideal gas model  to

compare  the  driS

 speed  with  the  random

 rms  speed

an  electron  would  have  at  20.0°C.  The  density  of

copper  is8.92  g/cm

3,  and  its  atomic  m

ass  is  63.5  u.

Circuits

•A  circuit  is  a  closed  path  of  som

e  sort  aroundwhich  current  circulates.•A  circuit  diagram

 can  be  used  to  represent  thecircuit.•Q

uan<<es  of  interest  are  generally  current  andpoten<al  diff

erence.

Sec<on  17.3

Meters  in  a  Circuit  –  A

mmeter

•An  am

meter  is  used  to  m

easure  current.–In  line  w

ith  the  bulb,  all  the  charge  passing  through  the  bulbalso  m

ust  pass  through  the  meter.

Sec<on  17.3

Meters  in  a  Circuit  –  Voltm

eter

•A  voltm

eter  is  used  to  measure  voltage  (poten<al

difference).

–Connects  to  the  two  contacts  of  the  bulb

Sec<on  17.3

Resistance

•In  a  conductor,  the  voltage  applied  across  theends  of  the  conductor  is  propor<onal  to  thecurrent  through  the  conductor.•The  constant  of  propor<onality  is  the  resistance  of  the  conductor.

Sec<on  17.4

Resistance,  Cont.

•Units  of  resistance  are  ohm

s  (Ω)

–1  Ω  =  1  V  /  A

•Resistance  in  a  circuit  arises  due  to  collisionsbetw

een  the  electrons  carrying  the  current  with

the  fixed  atoms  inside  the  conductor.

Sec<on  17.4

Ohm

’s  Law

•Experiments  show

 that  for  many  m

aterials,  includingmost  m

etals,  the  resistance  remains  constant  over  a

wide  range  of  applied  voltages  or  currents.•This  statem

ent  has  become  know

n  as  Ohm

’s  Law.

–ΔV  =  I  R•Ohm

’s  Law  is  an  em

pirical  rela<onship  that  is  validonly  for  certain  m

aterials.–M

aterials  that  obey  Ohm

’s  Law  are  said  to  be  ohm

ic.

Sec<on  17.4

Ohm

’s  Law,  Cont.

•An  ohm

ic  device•The  resistance  is  constantover  a  w

ide  range  of  voltages.•The  rela<onship  betw

eencurrent  and  voltage  is  linear.•The  slope  is  related  to  theresistance.

Sec<on  17.4

Ohm

’s  Law,  Final

•Non-­‐ohm

ic  materials  are

those  whose  resistance

changes  with  voltage  or

current.•The  current-­‐voltagerela<onship  is  nonlinear.•A  diode  is  a  com

mon  exam

pleof  a  non-­‐ohm

ic  device.

Sec<on  17.4

Resis<vity

•The  resistance  of  an  ohmic  conductor  is  propor<onal

to  its  length,  L,  and  inversely  propor<onal  to  its  cross-­‐sec<onal  area,  A

.

–ρ  is  the  constant  of  propor<onality  and  is  called  the  resis&vity  of  the  m

aterial.–See  table  17.1

Sec<on  17.4

Temperature  Varia<on  of  Resis<vity

•For  most  m

etals,  resis<vity  increases  with

increasing  temperature.

–With  a  higher  tem

perature,  the  metal’s

cons<tuent  atoms  vibrate  w

ith  increasingam

plitude.–The  electrons  find  it  m

ore  difficult  to  pass

through  the  atoms.

Sec<on  17.5

Temperature  Varia<on  of  Resis<vity,  Cont.

•For  most  m

etals,  resis<vity  increases  approximately

linearly  with  tem

perature  over  a  limited  tem

peraturerange.•–ρ  is  the  resis<vity  at  som

e  temperature  T

– ρo  is  the  resis<vity  at  som

e  reference  temperature  T

o

• To  is  usually  taken  to  be  20°  C

–

 is  the  temperature  coeffi

cient  of  resis5vity

–

Sec<on  17.5

Temperature  Varia<on  of  Resistance

•Since  the  resistance  of  a  conductor  with

uniform  cross  sec<onal  area  is  propor<onal  to

the  resis<vity,  you  can  find  the  effect  of

temperature  on  resistance.

•

Sec<on  17.5

Electrical  Energy  in  a  Circuit

•In  a  circuit,  as  a  charge  moves  through  the  baY

ery,  theelectrical  poten<al  energy  of  the  system

 is  increased  byΔQ

ΔV.–The  chem

ical  poten<al  energy  of  the  baYery  decreases  by  the

same  am

ount.

•As  the  charge  m

oves  through  a  resistor,  it  loses  thispoten<al  energy  during  collisions  w

ith  atoms  in  the

resistor.–The  tem

perature  of  the  resistor  will  increase.

Sec<on  17.6

(a)C

alculate the resistance per unit length ofa 22-gauge N

ichrome w

ire of radius 0.321m

m. (b

)If a potential difference of 10.0 V ism

aintained across a 1.00-m length of the

Nichrom

e wire, w

hat is the current in the wire?

(c)The w

ire is melted dow

n and recast with

twice its original length. Find the new

resistance RN as a m

ultiple of the oldresistance RO

.

Energy  Transfer  in  the  Circuit

•Consider  the  circuitshow

n.•Im

agine  a  quan<ty  ofposi<ve  charge,  

Q,

moving  around  the  circuit

from  point  A

 back  to  pointA.

Sec<on  17.6

Energy  Transfer  in  the  Circuit,Cont.

•Point  A  is  the  reference  point.

–It  is  grounded  and  its  poten<al  is  taken  to  bezero.•As  the  charge  m

oves  through  the  baYery  from

A  to  B,  the  poten<al  energy  of  the  system

increases  by  Q

V.–The  chem

ical  energy  of  the  baYery  decreases

by  the  same  am

ount.

Sec<on  17.6

Energy  Transfer  in  the  Circuit,  Final

•As  the  charge  m

oves  through  the  resistor,  from  C  to  D

,it  loses  energy  in  collisions  w

ith  the  atoms  of  the

resistor.•The  energy  is  transferred  to  internal  energy.•W

hen  the  charge  returns  to  A,  the  net  result  is  that

some  chem

ical  energy  of  the  baYery  has  been

delivered  to  the  resistor  and  caused  its  temperature  to

rise.

Sec<on  17.6

Electrical  Energy  and  Power,  Cont.

•The  rate  at  which  the  energy  is  lost  is  the

power.

•••From  Ohm

’s  Law,  alternate  form

s  of  power  are

••

Sec<on  17.6

Electrical  Energy  and  Power,  Final

•The  SI  unit  of  power  is  W

aY  (W

).–I  m

ust  be  in  Amperes,  R  in  ohm

s  and  V  in

Volts•The  unit  of  energy  used  by  electric  com

paniesis  the  kilow

a:-­‐hour.

–This  is  defined  in  terms  of  the  unit  of  pow

erand  the  am

ount  of  <me  it  is  supplied.

–1  kWh  =  3.60  x  10

6  J

Sec<on  17.6

Superconductors

•A  class  of  m

aterials  andcom

pounds  whose  resistances

fall  to  virtually  zero  below  a

certain  temperature,  T

C

– TC  is  called  the  cri<cal  tem

perature

•The  graph  is  the  same  as  a

normal  m

etal  above  TC ,  but

suddenly  drops  to  zero  at  TC

•

Sec<on  17.7

Superconductors,  Cont.

• The  value  of  TC  is  sensi<ve  to

–Chemical  com

posi<on–Pressure–Crystalline  structure•Once  a  current  is  set  up  in  a  superconductor,  it

persists  without  any  applied  voltage.

–Since  R  =  0

Sec<on  17.7

Superconductor  Timeline

•1911–Superconduc<vity  discovered  by  H

.  Kamerlingh  O

nnes•1986–H

igh  temperature  superconduc<vity  discovered  by  Bednorz  and  M

üller–Superconduc<vity  near  30  K•1987–Superconduc<vity  at  96  K  and  105  K•Current–Superconduc<vity  at  150  K–M

ore  materials  and  m

ore  applica<ons

Sec<on  17.7

Superconductor,  Final

•Good  conductors  do  not

necessarily  exhibitsuperconduc<vity.•One  applica<on  is  the

construc<on  ofsuperconduc<ng  m

agnets.•

Sec<on  17.7

Electrical  Ac<vity  in  the  H

eart

•Every  ac<on  involving  the  body’s  muscles  is

ini<ated  by  electrical  ac<vity.•Voltage  pulses  cause  the  heart  to  beat.•These  voltage  pulses  are  large  enough  to  bedetected  by  equipm

ent  aYached  to  the  skin.

Sec<on  17.8

Opera<on  of  the  H

eart

•The  sinoatrial  (SA)  node

ini<ates  the  heartbeat.•The  electrical  im

pulses  causethe  right  and  leS

 ar<al  muscles

to  contract.•W

hen  the  impulse  reaches

the  atrioventricular  (AV)  node,

the  muscles  of  the  atria  begin

to  relax.•The  ventricles  relax  and  thecycle  repeats.

Sec<on  17.8

Electrocardiogram  (EKG

)

•A  norm

al  EKG•P  occurs  just  before  the  atriabegin  to  contract.•The  Q

RS  pulse  occurs  in  theventricles  just  before  theycontract.•The  T  pulse  occurs  w

hen  thecells  in  the  ventricles  begin  torecover.

Sec<on  17.8

Abnorm

al  EKG,  1

•The  QRS  por<on  is  w

iderthan  norm

al.•This  indicates  thepossibility  of  an  enlargedheart.

Sec<on  17.8

Abnorm

al  EKG,  2

•There  is  no  constant  rela<onship  between  P  and  Q

RS  pulse.•This  suggests  a  blockage  in  the  electrical  conduc<on  pathbetw

een  the  SA  and  the  A

V  nodes.•This  leads  to  ineffi

cient  heart  pumping.

Sec<on  17.8

Abnorm

al  EKG,  3

•No  P  pulse  and  an  irregular  spacing  betw

een  the  QRS  pulses

•Symptom

a<c  of  irregular  atrial  contrac<on,  called  fibrilla&on•The  atrial  and  ventricular  contrac<on  are  irregular.

Sec<on  17.8

Implanted  Cardioverter  D

efibrillator(ICD

)•Devices  that  can  m

onitor,record  and  logically  processheart  signals•Then  supply  diff

erentcorrec<ve  signals  to  heartsthat  are  not  bea<ng  correctly

Sec<on  17.8

Func<ons  of  an  ICD

•Monitor  atrial  and  ventricular  cham

bers–D

ifferen<ate  betw

een  arrhythmias

•Store  heart  signals  for  read  out  by  a  physician•Easily  reprogram

med  by  an  external  m

agnet

Sec<on  17.8

More  Func<ons  of  an  ICD

•Perform  signal  analysis  and  com

parison•Supply  repe<<ve  pacing  signals  to  speed  up  orslow

 down  a  m

alfunc<oning  heart•Adjust  the  num

ber  of  pacing  pulses  per  minute

to  match  pa<ent’s  ac<vity

Sec<on  17.8