PHY 2049 Chapter 26 Current and Resistance. Chapter 26 Current and Resistance In this chapter we...
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Transcript of PHY 2049 Chapter 26 Current and Resistance. Chapter 26 Current and Resistance In this chapter we...
PHY 2049Chapter 26
Current and Resistance
Chapter 26 Current and Resistance In this chapter we will introduce the following new concepts:
-Electric current ( symbol i ) -Electric current density vector (symbol ) -Drift speed (symbol vd ) -Resistance (symbol R ) and resistivity (symbol ρ ) of a conductor -Ohmic and non-Ohmic conductors
We will also cover the following topics:
-Ohm’s law -Power in electric circuits
J
(26 - 1)
Physical Resistors
What Happens?
“+”
“+”
“+”
“+”
REMEMBER, THE ELECTRONS
ARE ACTUALLY MOVING THE
OTHER WAY!
What’s Moving?
What is making the charged move??
Battery
KEEP IN MIND 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=V/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.
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
i
+ q
conductor
v
i
- q
conductor
v
An electric current is represented by an arrow which has
the same direction as the charge velocity. The sense of the
current arrow is defined as follows:
If the current is due to t
Current direction :
1. he motion of charges
the current arrow is to the charge velocity
If the current is due to the motion of charges
the current arrow is to the charge veloci
t
vparallel
2.
ant
nega
iparallel
posit
tive
ive
y v
(26 - 3)
dqi
dt
UNITS
A current of one coulomb per second is defined as ONE AMPERE.
ANOTHER DEFINITION
A
I
area
currentJ
When a current flows through a conductor
the electric field causes the charges to move
with a constant drift speed . This drift speed
is superimposed on the random motion of the
charges.
dv
Drift speed
Consider the conductor of cross sectional area shown in the figure. We assume
that the current in the conductor consists of positive charges. The total charge
within a length is given by:
A
q L q nA . This charge moves through area
in a time . The current /
The current density
In vector form:
dd d
dd
d
L e A
L q nALet i nAv e
v t L v
nAv eiJ nv e
A A
J nev
dJ nev
dJ nv e
(26 - 5)
+ -
i
V
If we apply a voltage across a conductor (see figure)
a current will flow through the conductor.
We define the conductor resistance as the ratio
V the Ohm (symbol
A
V
Ri
V
i
SI
R
Unit for R :
esist ance
A conductor across which we apply a voltage = 1 Volt
and results in a current = 1 Ampere is defined as
having resistance of 1
Why not use the symbol "O" instead of " "
Suppose we ha d
)
V
i
Q :
A : a 1000 resistor.
We would then write: 1000 O which can easily
be mistaken read as 10000 .
A conductor whose function is to provide a
specified resistance is known as a "resistor"
The symbol is
given to the left.
V
Ri
(26 - 6)
R
Ohm’s Law
IRV
Graph
IRV
l
VV ab E
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.
E
+ -
i
V
E
Unlike the electrostatic case, the electric field in the
conductor of the figure is not zero. We define as
resistivity of the conductor the ratio
In vector form: E
J
J
E
Resi
SI u
stivit
nit r
y
fo
2
The conductivity is defined as:
Using the previou
V/m V m m
A/m
s equation takes the for
1
m
A
: J E
ρ :
Consider the conductor shown in the figure above. The electric field inside the
conductor . The current density We substitute and into
/ equation and get:
/
V iE J E J
L AE V L V A A
RJ i A i L L
L
RA
LR
A
E J
J E
(26 -7)
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
)(1 00 TT
Range of and
REMEMBER
IRVA
LR
TemperatureEffect
T
)1(0 T
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
If the device connected to the battery is a resistor R then the energy transfered by the
battery is converted as that appears on R. If we combine the equation
with Ohm's law: , we
P iV
Vi
R
heat
22
get the following two equivalent expressions for
the rate at which heat is dissipated on R.
and
VP i R P
R
V2 P i R
2
V
PR
(26 - 13)