Download Electric Current - Engineering Physics - Lecture Slides and more Slides Engineering Physics in PDF only on Docsity!
Todayās agenda:
Electric Current. You must know the definition of current, and be able to use it in solving problems.
Current Density. You must understand the difference between current and current density, and be able to use current density in solving problems.
Ohmās Law and Resistance. You must be able to use Ohmās Law and electrical resistance in solving circuit problems.
Resistivity. You must understand the relationship between resistance and resistivity, and be able to calculate resistivity and associated quantities.
Temperature Dependence of Resistivity. You must be able to use the temperature coefficient of resistivity to solve problems involving changing temperatures.
Electric Current
Definition of Electric Current
The average current that passes any point in a conductor during a time ļt is defined as
where ļQ is the amount of charge passing the point.
One ampere of current is one coulomb per second:
av
Q
I
t
The instantaneous current is
dQ
I =.
dt
1C
1A =
1s
+ -
current electrons
An electron flowing from ā to +
āConventionalā refers to our convention, which is always to consider the effect of + charges (for example, electric field direction is defined relative to + charges).
An electron flowing from ā to + gives rise to the same āconventional currentā as a proton flowing from + to -.
āHey, that figure you just showed me is confusing.
+ -
current electrons
Good question.
āHey, that figure you just showed me is confusing. Why donāt electrons flow like this?ā
Note!
Current is a scalar quantity, and it has a sign associated with it.
In diagrams, assume that a current indicated by a symbol and an arrow is the conventional current. (^) I 1
If your calculation produces a negative value for the current, that means the conventional current actually flows opposite to the direction indicated by the arrow.
Example: 3.8x10^21 electrons pass through a point in a wire in 4 minutes. What was the average current?
av
Q Ne
I
t t
21 19 av
I
ļ“ ļ“^ ļ
Iav ļ½ 2.53A
Current Density
When we study details of charge transport, we use the concept of current density.
Current density is the amount of charge that flows across a unit of area in a unit of time.
Current density: charge per area per time. docsity.com
A current density J flowing through an infinitesimal area dA produces an infinitesimal current dI.
dA
J
dI ļ½ J dAļ
The total current passing through A is just
surface
I ļ½ (^) ļ² J dAļ
Current density is a vector. Its direction is the direction of the velocity of positive charge carriers.
Current density: charge per area per time.
No OSEās on this page. Simpler, less-general OSE on next page.
The total amount of charge passing through A is the number of charges times the charge of each.
v A
vļt
q
ļQ ļ½ nqv t Aļ
Divide by ļt to get the currentā¦
Q
I nqv A
t
ā¦and by A to get J:
J ļ½nqv.
To account for the vector nature of the current density,
J ļ½nqv
and if the charge carriers are electrons, q=-e so that
J e ļ½ ļn e v.
The ā sign demonstrates that the velocity of the electrons is antiparallel to the conventional current direction.
āofficialā yet.^ Not quite
Not quite āofficialā yet.
E electron ādriftā velocity
The voltage accelerates the electron, but only until the electron collides with a āscattering center.ā Then the electronās velocity is randomized and the acceleration begins again.
Some predictions based on this model are off by a factor or 10 or so, but with the inclusion of some quantum mechanics it becomes accurate. The āscatteringā idea is useful.
A greatly oversimplified model, but the āideaā is useful.
just one electron shown, for simplicity
inside a conductor
Even though the details of the model on the previous slide are wrong, it points us in the right direction, and works when you take quantum mechanics into account.
In particular, the velocity that should be used in
J ļ½n q v.
is not the charge carrierās velocity (electrons in this example).
Instead, we should the use net velocity of the collection of electrons, the net velocity caused by the electric field.
This ānet velocityā is like the terminal velocity of a parachutist; we call it the ādrift velocity.ā
J ļ½n q v .d
Quantum mechanics shows us how to deal correctly with the collection of electrons.
Example: the 12-gauge copper wire in a home has a cross- sectional area of 3.31x10-6^ m^2 and carries a current of 10 A. The conduction electron density in copper is 8.49x10^28 electrons/m^3. Calculate the drift speed of the electrons.
d
I
v
nqA
d
I
v
neA
d (^28) -3 19 6 2
10C/s
v
(8.49 10 m )(1.60 10 ļ^ C)(3.31 10 ļ m )
4
vd 2.22 10 m/s
āQuizā time (maybe for points, maybe just for practice!)
