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Resistance in a Conductor
There are three external factors that influence the resistance in a
conductor.
Thickness (cross sectional area of the wire), length, and
temperature all have some effect on the amount of resistance created in
a conductor. The fourth factor is the conductivity of the material we
are using. Some metals are just more electrically conductive than
others. This however, is considered an internal factor rather than an
external one.
Cross Sectional Area
The cross-sectional area of a conductor (thickness) is similar to the
cross section of a hallway.
If the hall is very wide, it will allow a
high current through it, while a narrow hall would be difficult to get
through due to it's restriction to a high rate of flow.
The animation
at the left demonstrates the comparison between a wire with a small cross
sectional area and a larger one.
Notice that the electrons seem to be
moving at the same speed in each one but there are many more electrons
in the larger wire.
This results in a larger current which leads us
to say that the resistance is less in a wire with a larger cross sectional
area.
Length of the Conductor
The length of a conductor is similar to the length of a hallway.
A
shorter hallway would allow people to move through at a higher rate than
a longer one.
Temperature
The temperature of a conductor has a less obvious effect on the resistance
of the conductor. It would be as hard to apply the hallway analogy as
it is hard to say whether a hot hallway would make us move faster or slower
than a cold hallway.
To truly understand the effect you must picture
what happens in a conductor as it is heated.
Remember, heat on the
atomic or molecular scale is a direct representation of the vibration of
the atoms or molecules.
Higher temperature means more
vibrations.
Imagine a hallway full of people.
Half of the people the
electrons are trying to move in the same direction you are and the other
half the protons are evenly spaced but stationary in the hallway.
This
would represent a cold wire.
Since the wire is cold the protons are not
vibrating much so the electrons can run between them fairly rapidly.
As
the conductor (hallway) heats up, the protons start vibrating and moving
slightly out of position.
As their motion becomes more erratic they are
more likely to get in the way and disrupt the flow of the electrons. As
a result, the higher the temperature, the higher the resistance.
A prime
example of this is when you turn on a light bulb.
The first instant,
the wire filament is cold and has a low resistance but as the wire heats
up and gives off light it increases in resistance.
As a result we can
say that Ohm's law holds true unless temperature changes.
At extremely low temperatures, some materials have no measurable
resistance.
This is called superconductivity.
The materials are
known as superconductors.
Gradually, we are creating materials that
become superconductors at higher temperatures and the race is on to find
or creates materials that superconductor at room temperature.
We are
painfully far away from the finish line.
In conclusion, we could say that a short fat cold wire makes the best
conductor.
Electrical resistance
Voltage can be thought of as the pressure pushing charges along a conductor,
while the electrical resistance of a conductor is a measure of how
difficult it is to push the charges along. Using the flow analogy,
electrical resistance is similar to friction. For water flowing through
a pipe, a long narrow pipe provides more resistance to the flow than does
a short fat pipe. The same applies for flowing currents: long thin wires
provide more resistance than do short thick wires.
The resistance (R) of a material depends on its length, cross-sectional
area, and the resistivity (the Greek letter rho), a number that depends
on the material:
The resistivity and conductivity are inversely related. Good conductors
have low resistivity, while poor conductors (insulators) have
resistivities that can be 20 orders of magnitude larger.
Resistance also depends on temperature, usually increasing as the
temperature increases. For reasonably small changes in temperature, the
change in resistivity, and therefore the change in resistance, is
proportional to the temperature change.
Ohm's Law
In many materials, the voltage and resistance are connected by Ohm's Law:
Ohm's Law : V = IR
The connection between voltage and resistance can be more complicated in
some materials.These materials are called non-ohmic. We'll focus mainly
on ohmic materials for now, those obeying Ohm's Law.
Electric power
Power is the rate at which work is done. It has units of Watts. 1 W = 1
J/s
Electric power is given by the equations:
The power supplied to a circuit by a battery is calculated using P = VI.
Batteries and power supplies supply power to a circuit, and this power
is used up by motors as well as by anything that has resistance. The power
dissipated in a resistor goes into heating the resistor; this is know as
Joule heating. In many cases, Joule heating is wasted energy. In some cases,
however, Joule heating is exploited as a source of heat, such as in a
toaster or an electric heater.
The electric company bills not for power but for energy, using units of
kilowatt-hours.
1 kW-h = 3.6 x 106 J
Although power is cheap, it is not limitless. Electricity use continues
to increase, so it is important to use energy more efficiently to offset
consumption. Appliances that use energy most efficiently sometimes cost
more but in the long run, when the energy savings are accounted for, they
can end up being the cheaper alternative.
Resistivity
The electrical resistance of a wire would be expected to be greater for
a longer wire, less for a wire of larger cross sectional area, and would
be expected to depend upon the material out of which the wire is made.
Experimentally, the dependence upon these properties is a straightforward
one for a wide range of conditions, and the resistance of a wire can be
expressed as