Transcript P5: Resistors and Current.

2/2009
EXAMINATION #2
WEDNESDAY MARCH 4, 2009
“+”
REMEMBER, THE ELECTRONS
“+”
ARE ACTUALLY MOVING THE
OTHER WAY!
-
“+”
“+”
Battery


A wire is a conductor
We will assume that the conductor is
essentially an equi-potential
◦ It really isn’t.

Electrons are moving in a conductor if a
current is flowing.
◦ This means that there must be an electric field in
the conductor.
◦ This implies a difference in potential since
E=DV/d
◦ We assume that the difference in potential is
small and that it can often be neglected.
◦ In this chapter, we will consider this difference
and what causes it.

Current is the motion of POSITIVE CHARGE
through a circuit. Physically, it is electrons
that move but …
Conducting material
DQ,Dt
Conducting material
DQ,Dt
CURRENT
DQ
i
Dt
or
dq
i
dt

A current of one coulomb per second is
defined as ONE AMPERE.
A charged belt, 30 cm wide, travels at 40 m/s
between a source of charge and a sphere. The belt
carries charge into the sphere at a rate
corresponding to 100 µA. Compute the surface
charge density on the belt.
[8.33e-06] C/m2
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?
An electric current is given by the expression I(t) = 100
sin(120πt), where I is in amperes and t is in seconds. What is
the total charge carried by the current from t = 0 to t =
(1/240) s?
current I
J

area
A
The figure 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?





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: DV=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.
DV  IR
DV  IR
Resistance Varies with Applied Voltage
(actually with current)




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 ……
+
-
Vb  Va
E
l
A.
B.
C.
D.
E.
wq
2pwq
wq/2p
4pwq
You need the radius to answer this
question
A circular wire (Radius=R) carries a current I and the current density is
J=br.
Find the value of the total current.
dA  2prdr
dI  JdA  br  2prdr  2pbr 2 dr
R
2
I   2pbr dr  pbR 3
3
0
2


Electrons are going the opposite way from
the current. (WHY?)
They probably follow a path like …
Average “drift”
speed - vd
IN
OUT





vd average drift velocity of the electron
n number of electrons (mobile) per unit
volume.
Dt interval of time
Dx average distance the electron moves in
time Dt.
Q total amount of CHARGE that goes
through a surface of the conductor in time Dt.
The Diagram
DQ  (nAvd Dt )e
DQ
I avg 
 nAvd e
Dt
I avg
J
 nevd
A
J  nev d
Often a Vector





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”.
We showed two slides ago:
v  v0  at  at
F eE
a 
m m
eE
v  vd 

m
Let n= number of charge carriers
per unit volume (mobile electrons)
eE
J  nqvd  nevd  ne 
m
or
ne 2 E
J
  E
m
so
ne 2

m
1


resistivity
  vd
The average drift velocity of an
electron is about 10-4 m/s
How can a current go through a resistor and
generate heat (Power) without decreasing the
current itself?
Loses Energy
Gets it back
Exit
In metals, the bigger the electric field at a
point, the bigger the current density.
J  E
 is the conductivity of the material.
=(1/) is the resistivity of the material
  0 1   (T  T0 )
A conductor of uniform radius 1.20 cm carries a
current of 3.00 A produced by an electric field of
120 V/m. What is the resistivity of the material?
DV  El
1 DV I
J  E 
 (def)
 l
A
l
DV  I
A
l
R
A
DV  V  IR
R
L
A
DV  IR
D
DT
  0 (1  DT )
In time Dt, a charge DQ is pushed through
the resistor by the battery. The amount of work
done by the battery is :
DW  VDQ
Power :
DW
DQ
V
 VI
Dt
Dt
Power  P  IV  I IR   I 2 R
E2
P  I R  IV 
R
2
that’s it, Doc