Electrical Current
Inexact definition: The rate of flow of charge
How would you make this definition more precise ?
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Although the charge flowing is electron charge (i.e. negative
charge), the direction of electric current is defined as the
direction of flow of positive charge
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Electrical Current
Inexact definition: The rate of flow of charge
How would you make this definition more precise ?
Lets consider the following “thought experiment”.
You want to count the number of fish flowing down a river.
You would:
pick a location on the river,
then define a cross-sectional area (perpendicular to the flow of the water)
and then you would count the “net flow” by counting:
The number of fish swimming down river
The number of fish swimming up river.
Definition: The rate of net flow of electric charge through a crosssectional area that is perpendicular to the direction of flow.
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Electrical Current
Definition: The rate of net flow of electric charge through a crosssectional area A that is perpendicular to the direction of flow.
In the drawing below to get the net flow of charge to the right:
add up all the positive charge flowing to the right
continue adding negative charge flowing to the left
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A Model for Electric Current
Lets denote the net charge flowing through this area A
in a time interval t as: Q
The electric current is then:
I=
Q
t
The instantaneous current is obtained by considering smaller and
small time intervals, i.e.
I=lim t 0
Q dQ
=
t
dt
The units for current is called an “Ampere”. Ampere is a derived unit.
1C
1 A=
1s
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Electrical Current
Definition: The rate of net flow of electric charge through a crosssectional area A that is perpendicular to the direction of flow.
In the drawing below to get the net flow of charge to the right:
add up all the positive charge flowing to the right
continue adding negative charge flowing to the left
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In electrolytes (like battery fluid), there can be both positive and
negative charge carriers.
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Relating Macroscopic (electrical current) to
Microscopic (density of charge carriers)
Consider a section of the cylindrical wire below of length x
In time t a charge carrier moves a distance x =v d t
Here v d is called the “drift velocity” of the charge carrier.
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Consider a section of the cylindrical wire below of length
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Relating Macroscopic (electrical current) to
Microscopic (density of charge carriers)
Lets say we know the microscopic density of charge carriers n
(this would be the number of charge carriers per unit volume)
and the charge on each charge carrier.
We want to derive an expression for the macroscopic current I =
Q
t
x
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Relating Macroscopic (electrical current) to
Microscopic (density of charge carriers)
The total charge in the section of interest:
Q=number of charge carriers x charge per carrier = n A x q
Q=n A v d t q
or
I=
Q
=n A v d q
t
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The current is proportional to the cross-sectional area of the wire.
All the other quantities in the equation are microscopic quantities.
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Relating Macroscopic (electrical current) to
Microscopic (density of charge carriers)
The current is proportional to the cross-sectional area of the wire.
All the other quantities in the equation are microscopic quantities.
So we can define a “current density”
I
J = =n v d q
A
which consists of only microscopic quantities
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Example 21.1
Drift speed in a copper wire
12-gauge copper wire in a typical residential building has a cross-sectional
area of 3.3 x 10-6 m2.
If it carries a current of 10 A, what is the drift speed of the electrons ?
Assume that each copper atom contributes one free electron to the current.
Take the density of copper as 8.95 g/cm3.
Also known:
Atomic mass of copper is 63.5 g/mole
One copper atom has 29 protons and 34 neutrons
So one copper atom has how many electrons ??
Do in class
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Electrical Resistance
Definition: The electrical resistance of a conductor is the ratio of the
potential difference across it to the current that flows as a result of that
potential difference.
R=
V
I
It turns out that for a conductor that the relationship
between current and the potential difference is linear.
Slope is 1/R
For a semiconductor this relationship is not linear.
The “resistance” is larger for smaller currents than for
large ones.
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Electrical Resistance
Definition: The electrical resistance of a conductor is the ratio of the
potential difference across it to the current that flows as a result of that
potential difference.
R=
V
I
It turns out that for a conductor that the relationship
between current and the potential difference is linear.
Slope is 1/R
For a semiconductor this relationship is not linear.
The “resistance” is larger for smaller currents than for
large ones.
For an insulator, this resistance is very large.
For a superconductor, the “resistance” is very small.
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