chapter27 - Chapter 27 Current Resistance And Resistor...

Chapter 27
Current
Resistance
And
Resistor

Electric Current, the definition

Assume charges are
moving perpendicular to a
surface of area A

If Δ Q is the amount of
charge that passes
through A in time Δ t , then
the average current is
t
Q
I
avg
∆
∆
=
or
dt
dQ
I =
+
+
+ +
+
+
I
A
Anyone notices a difference of this figure
compared with the one in the book?
If yes, and plain why I draw it this way.
Correct answer = 1 bonus point
How many of you preview, review, do
homework within 2 days of class, 2 days
toward due date?

Electric Current, definition and unit

Electric current is the rate of flow of charge
through some region of space

The SI unit of current is the ampere (A)

1 A = 1 C / s

And ampere is a base unit. The unit for time,
second, is also a base unit.

The unit for charge is then defined as 1C=1A/1s

The symbol for electric current is I

Direction of Current

The charges passing through the area could be
positive or negative or both. This area may or may
not be an actual physical surface and the charges
can flow in a conductor or in vacuum.

It is conventional to assign to the current the same
direction as the flow of positive charges

The direction of current flow is opposite the direction
of the flow of electrons

It is common to refer to any moving charge as a
charge carrier

Current in a conductor and the
drift speed

Charged particles move through
a conductor under the drive of
an electric field inside.

Assume a cross-sectional area A
that is perpendicular to and the
number of charge carriers per
unit volume n.

Then nA Δ x is the total number of
charge carriers
Wait!
There should be no electric field inside a
conductor. Explanation please!
E
d
V


Current linearly proportional to drift
speed

The total charge is the number of carriers times the
charge per carrier, q

Δ Q = ( nA Δ x ) q

The drift speed, v
d
, is the speed at which the carriers
move

v
d
= Δ x / Δ t and ∆ x = v
d
∆ t

Rewritten: Δ Q = ( nAv
d
Δ t ) q

Finally, current, I
ave
= Δ Q / Δ t = nqv
d
A

This is to say that current is linearly proportional to
the drift speed v
d

A typical value of the drift speed

Assume a copper wire, with one free electron per
atom contributed to the current

The drift speed for a 12-gauge copper wire carrying
a current of 10.0 A is
2.23 x 10
-4
m/s

This is a typical order of magnitude for drift speeds

This is very slow, how come when a switch is close,
the light comes on from a light bulb ~ 10m away? It
should take ~10/ 2.23 x 10
-4
sec which is about 12
hours.

What is wrong?

Motion of the charge carrier, the electrons,
in a conductor

The actual charge carrier in conductor is
the electron

The zigzag black lines represents the
motion of a charge carrier in a
conductor

The net drift speed is small

The sharp changes in direction are due
to collisions

The net motion of electrons is opposite
the direction of the electric field

The current direction is conventionally
defined to be the positive carrier motion
direction, or the electric field direction.