Current and ResistanceCurrent and Resistance
October 9, 2006October 9, 2006
Notes Notes
New topic today – Current and New topic today – Current and ResistanceResistance
Quiz on FridayQuiz on FridayFriday 7:30 review sessiomn.Friday 7:30 review sessiomn.There is a new WebAssign.There is a new WebAssign.
Is it AM or PM … only the shadow knows Is it AM or PM … only the shadow knows for sure.for sure.
I know too.I know too.
New Topic:Current and Resistance
Physical Resistors
More …
What Happens?
“+”
“+”
“+”
“+”
REMEMBER, THE ELECTRONS
ARE ACTUALLY MOVING THE
OTHER WAY!-
-
DEFINITION
Current is the motion of POSITIVE CHARGE through a circuit. Physically, it is electrons that move but …
Conducting material
Q,t
Conducting material
Q,t
dt
dqi
ort
Qi
CURRENT
UNITS
A current of one coulomb per second is defined as ONE AMPERE.
A small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of rotation is ω. What average current does this rotating charge represent?
Fraggen …..
ANOTHER DEFINITION
A
I
area
currentJ
Figure P27.8 represents a section of a circular conductor of non-uniform diameter carrying a current of 5.00 A. The radius of cross section A1 is 0.400 cm. (a) What is the magnitude of the current density across A1? (b) If the current density across A2 is one-fourth the value across A1, what is the radius of the conductor at A2?
Ohm A particular object will resist the flow of current.
It is found that for any conducting object, the current is proportional to the applied voltage.
STATEMENT: V=IR R is called the resistance of
the object. An object that allows a
current flow of one ampere when one volt is applied to it has a resistance of one OHM.
Graph
A DIODE
Resistance Varies with Applied Voltage (actually with current)
Let’s look at the atomic level ..
Conduction is via electrons. They are weak and small and don’t exercise
much. Positive charge is big and strong and doesn’t
intimidate easily. It’s an ugly situation … something like ……
-
+
Consider a metal conductor
So far, we have said that a metal is an equipotential because no charges were moving. Hence, no electric field in the metal You can move a charge freely in the metal BECAUSE there
is no electric field.
NOW we have a current. This can only happen if we allow an electric field to push
the charges. Thus, the metal is NO LONGER A TRUE
EQUIPOTENTIAL. But almost …. as we shall see in the next chapter.
l
VV ab E
The Current
Electrons are going the opposite way from the current. (WHY?)
They probably follow a path like …
Average “drift”speed - vd
OUTIN
Notation
vd average drift velocity of the electron n number of electrons (mobile) per unit
volume. t interval of time x average distance the electron moves
in time t. Q total amount of CHARGE that goes
through a surface of the conductor in time t.
dvJ ne
nevA
IJ
enAvt
QI
etnAvQ
davg
davg
d
)(
Often a Vector
The Diagram
We return to the diagram ….. Consider an electron. Assume that whenever it
“bumps” into something it loses its momentum and comes to rest.
It’s velocity therefore starts at zero, the electric field accelerates it until it has another debilitating collision with something else.
During the time it accelerates, its velocity increases linearly .
The average distance that the electron travels between collisions is called the “mean free path”.
Starting when the electron is at rest:
m
eEvv
m
eE
m
Fa
atatvv
d
0
Let n= number of charge carriersper unit volume (mobile electrons)
We showed two slides ago::
1
2
2
m
ne
so
Em
EneJ
orm
eEnenevnqvJ dd
Finally
dv
Reference
The average drift velocity of an electron is about 10-4 m/s
Ponder
How can a current go through a resistor and generate heat
(Power) without decreasing the current itself?
Loses Energy
Gets it back
Exit
Conductivity
In metals, the bigger the electric field at a point, the bigger the current density.
EJ is the conductivity of the material.
=(1/) is the resistivity of the material
Going to the usual limit …
JdAI
anddA
dIJ
Example
A cylindrical conductor of radius R has a current density given by
(a) J0 (constant)
(b) r
Find the total current in each case.
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Range of and
Ye old RESISTANCE
IRVVA
lR
IA
lV
A
I
l
VE
El
VEJ
ElV
11
REMEMBER
IRVA
LR
A closed circuit
Power
R
EIVRIP
RIIRIIVPPower
VIt
QV
t
22
2
W
:Power
QVW
:isbattery by the done
workofamount The battery. by theresistor the
throughpushed is Q charge a t, In time
Ponder
How can a current go through a resistor and generate heat
(Power) without decreasing the current itself?
Loses Energy
Gets it back
Exit
A Circuit
)( rR
EI
E=emf