Ch. 27 Current and Resistance

HW: Chapter 27(14p,22E,50E), Chapter 28(10E,38E) Due on Oct.11,1999

§ 27-2 Electric Current (Flow of Charges)

•전류 :

t

dttiqdt

dqi

0 )(

: 전류는 Scalar. :화살표는 단지 전류의 방향만 표시

The total currents A,B and C are the same. But, the current density(J=1/A) are not the same

•Current charge Conservation

)( 210210

210

qqqdt

dq

dt

dq

dt

dqiii

: Point A 로 들어오는 전류는 A 에서 나가는 전류와 같다 .

§ 27-3 Current density

Current density

AJ

vvJ

di

nqA

i

city)drift velo : (

fluxnumber :

density)number :(

)/(

v vJ nqnq

n

nqvvLA

nALq

tA

q

A

iJ

§ 27-4 Resistance & Resistivity

•Resistance :

dependentgeometry

)/( of definition : AVRi

VR

•Resistivity :

tindependengeometry :

of definition :

JE

J

E

•Resistivity Resistance

L

AR

Ai

LV

J

E

/

/

A:area

• Conductivity :

EJ

1

yresistivit oft coeeificne eTemperatur :

)()(

eTemperatur with ofVariation

000

TTT

§ 27-5 Ohm’s Law

JE iRV

Both linear (cf.. Ohm’s law 가 적용되는 물질은 ohmic material)

V

i

J

E

e e

E

i

i+ -

: Charge carrier 는 전자: 관습적으로 I 의 방향은(+) 에서 (-)

V

slope)(

§ 27-7 Power in Electric Circuits

Power :

R

VRiiVP

iVdt

Vdq

dt

dWP

22

Power dissipation : battery 의 energy 를저항을 통해 소모 Joule heating;Ohm’s dissipation

• Extension of the Ohm’s law :BvJE

Later with B field• Nonlinear(I,V) 특성 : (Non Ohm’s law)

§ 27-9 superconductors

Tc : 4K

T(K)

수은

Tc : 4.12K

일정한 온도 ( 임계온도 ) 이하로 물체의 온도를 낮추면물체의 저항이 급격히 0 으로떨어지는 물질(BCS theory:1972 Nobel Prize)

SnNbTi/Nb3

low-TcS.C.

Tc = 0.5 (Ti 경우 ) = 3.7 (Sn 경우 ) = 8.0 (Nb 경우 )

LN(77K)LHe(4K)

§27-8 Semiconductor

)(

1)(

2 Tnne

mT

Temperature dependence

반도체에서 n(T) 는 매우 작지만온도가 올라감에 따라 급격히 증가 .따라서 온도가 증가하면 (conductivity) 증가(1956 Nobel prize Shockely-Bardenn Brattain)

Ch. 28 Circuits

HW: (15,64) Due 10/9 (Sol : 10/13)

§ 28-1 Emf(Electro-motive-force) : 기전력 ( 起電力 )

CF)Mmf (magnetic-motive-force)pmf (pondero-motive-force)smf (spin-motive-force)

§ 28-2 Work,Energy,and emf

it. move to charge the

on done work ofamount :

V

dq

CI

dq

dW

§ 28-3 Calculating the current in a single-loop circuit

1. Energy method

dtRidtPdW

dtidqdW

ε2

iR

Ri

2. Potential method(scanning clockwise from a to a)

aa ViRV

Ri

• Sign convention

For R – sign if the scan direction is along with the assumed current directionFor + sign for the going from – to +

§ 28-4 OTHER Single-loop circuits

aa VV iriR

2. Scan closed loop(clockwise) from point a

rRi

1.

aa ViRiRiRV 321

Rri

Rrri

21

21 1.

Rrri

ViRirirV cc

21

21

2211

2.

aV

bV

cV

12

aV

Rrri

Rrri

21

21

212 )(

I

2ir2ir

iR

1ir)( 2 Rri

)( 12 rRri

Fig: A graph of the potentials encountered in traversing this circuit clockwise from point a

§ 28-5 (Sample Prob.1)

mA240)(

)(

0

21

21

1122

Rrri

iriRir

1. from point a

2. from point b clockwise

ba

ab

VVi

VirV

011

§ 28-6 Multi loop circuits

bpoint than potentialhigher at is CPoint

0

0, ? 3.

, determinecan weeq.1,2 from

0

0

clockwise) apoint (from rule Potential 2.

ruleJunction : bat 1.

2

2

33222

21

23322

11231

231

cb

cb

bb

cb

VV

VV

VRiRiV

VV

ii

RiRi

RiRi

iii

• Resistance in Series or Parallel

Equivalent

n

jjeq RR

1

Series

ParallelEquivalent

n

j jeq RR 1

11

eq

n

j

n

j jjjj RRR

iR

i1

1

1 1

rR

RR

RRi

row

roweqrow

eqw

row

5000

, 5000 140

1

§ 28-8 RC circuits

1. Charging capacitor

constant] time: [

]0)0([ )1(

)()( and , 0

)()(

RCeRdt

dqi

tqecq

c

q

dt

dqR

dt

tdqti

c

tqRti

RCt

RCt

I 가 크면 charging time 이 크다 .

0)0( ,

,

0

max

qtt

cqt 0)( ,

)0( , 0

itRqt

# Note : Battery 에 의한 potential difference 와 capacitor 양단의 potential difference q(t)/c 가 같아질 때까지 charging 이 되고 전류가 흐른다 .

2. Discharging capacitor

)decreasing is charge scapacitor' that means (

capacitor) on the charge initial : (

0

0

000

RCt

RCt

eRC

q

dt

dqi

cVqeqq

c

q

dt

dqR