phy202_5

1
Lesson 5
Lesson 5
Current and Resistance

• Batteries
• Current Density
• Electron Drift Velocity
• Conductivity and Resistivity
• Resistance and Ohms Law
• Temperature Variation of Resistance
• Electrical Power and Joules Law
• Classical Model of Conduction in Metals

2
Electrical Resistance

• Electrical Resistance is
• friction to the flow of electric charge
• Observed in Conductors and
• Non Conductors
• Not found in Super Conductors

3
Charge Pump I
Capacitor will send current through load
resistance and loose charge
Load Resistance
I
-

4
Charge Pump I
Battery will send current through load
resistance and not loose charge
Charge in battery is regenerated by Chemical
reactions
Load Resistance
I
-

5
Flow of Charge
6
Current Picture
I
7
Current Picture Definition I
Current is the rate of Flow of positive charge
through whole cross sectional area of conductor
8
Current Picture Definition II
9
Conservation of Current
Current is Conserved
I1
I1I2
I2
I1
10
Driving force for Current

• Flowing charge experiences friction
• Work must be done to overcome friction
• Need driving force, hence need
• Electric Field
• Potential Difference

11
SI units
Potential Difference
Electrical Resistance


Current
V

R
I


V
V





W
R

(
Ohm
)


I
A
12
V-I plots
I-V plots
slope constant 1/R
slope not constant
I
I
V
V
Ohmic Material
Non Ohmic Material
13
Resistance I
Ohmic Materials

V
RI
Ohms
Law
V


R
constant
I
14
Resistance II
Non Ohmic Materials
R is not Constant, but varies with current and
voltage
15
Power
Power rate of doing work by applied force
dU
dQ


Power


V
IV
dt
dt
C
Nm
Nm










Power
I
V
AV
s
C
s
J

)
W

(
Watts
s
16
Ohmic Materials I
17
Ohmic Materials II
For Ohmic Materials

• Resistance is proportional to length of
  conductor
• Resistance is inversely proportional to the
  cross sectional area of the conductor

18
Resistivity
19
Picture
l
I
a
V-
V
E
20
Current Density

-

V
V
V
El

-
V
El
Ea



I
l
r
R
r
a

Divide by Area Current Density magnitude
Current per cross sectional area
I
E
J
s
E



r
a
1
s



conductivity
r
21
Integral Formula
22
Electrical Conduction
Classical Microscopic Theory of Electrical
Conduction
23
Random Walk
24
Picture
25
Definition of Variables
Charge in Volume
D
V
D
Q
nA
x q
nAv
t q

D

D
d
n
number of charge carriers

per unit volume
A
cross sectional area

q
amount of charge on

each carrier
D
x
average distance moved in

D
time
t
after collision
v

drift velocity
d
26
Equations I
D
Q
D
x

nA
q
D
t
D
t
dQ
q
Þ

I

nAv
dt
d
Þ
J

nv
q
d
J
Þ

v
nq
d
27
Equations II
acceleration of charge
q
in field
E
q

a
E
m

• Let t

average time between collisions

• at each collision charge carrier

forgets

drift velocity
,
so we can take initial drift
\
velocity

0
and
just before collisions
æ
ö
q
q

t

t

t
ç

v
a
E
E
è
ø
d
m
m
J
q


t
v
E
d
nq
m
2
t
nq
Þ

J
E
m
2
t
nq
Þ
s

m
28
Temperature Effects
Temperature Effects
1
m
r


s
nq
t
2
As temperature increases
t
decreases
thus
r
increases


(
)
(
)
r
T

r
1

a
T
-
T
0
0
1
d
r
a


Temperature Coefficient of Resistivity
r
dT

0
29
Temperature Effects




(
)
(
)
r
T

r
1

a
T
-
T
0
0
1
d
r
a


Temperature Coefficient of Resistivity
r
dT
Equation

0
Thus


(
)
(
)


a
-
T
T
R
T
R
1
0
0