Electrical Resistance
Electrical Resistance is one of the easiest aspects to understand  SOURCE
Resistance
For most materials, there is a simple relationship between the potential
difference applied across two points and the current generated. An Ohmic
material is one for which the potential difference and current are related as
below:
Figure 9.4: Voltage vs. current for an Ohmic
material

For such materials the voltage and current are proportional  doubling the
potential difference doubles the current. The constant of proportionality is
called the resistance, which is defined through Ohm's law:
The units of resistance are Volts / Ampères, or Ohms ().
Thus, for a given potential difference, materials with a high resistance will
allow a small current relative to a material with a low resistance.
In analogy with heat resistance and conductivity, one can define an electrical
conductivity as being proportional to the inverse of the resistance. Thus,
good electrical conductors, such as copper, have a low resistance, and poor
electrical conductors, such as concrete, have a high resistance.
At the atomic level, currents are pictured as the flow of the outer
electrons of atoms through the material. Resistance then results from collisions
of electrons with other electrons and with atoms. From this we would expect that
raising the temperature of a material would increase the resistance, as the
added heat energy would cause the electrons to move faster and hence collide
more often. This is indeed what is generally observed.
Elementary Principles 
SOURCE
Resistance

The electrical resistance of a circuit component or device
is defined as the ratio of the voltage
applied to the electric
current whichflows through it:
If the resistance is constant over a considerable range of
voltage, then Ohm's
law, I = V/R, can be used to predict the behavior of the
material. Although the definition above involves DC current and
voltage, the same definition holds for the AC
application of resistors.

Whether or not a material obeys Ohm's law, its resistance can be
described in terms of its bulk resistivity. The
resistivity, and thus the resistance, is temperature dependent. Over
sizable ranges of temperature, this temperature dependence can be
predicted from a temperature
coefficient of resistance.




Resistivity and Conductivity
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
The factor in the resistance which takes into account the nature of
the material is the resistivity . Although it is temperature dependent,
it can be used at a given temperature to calculate the resistance of a
wire of given geometry.
The inverse of resistivity is called conductivity. There are
contexts where the use of conductivity is more convenient.
Electrical conductivity = s
= 1/r




Resistivity Calculation
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 (resistivity).
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
Enter data and then click on the quantity you wish to calculate in
the active formula above. Unspecified parameters will default to values
typical of 10 meters of #12 copper wire. Upon changes, the values will not
be forced to be consistent until you click on the quantity you wish to
calculate.
Standard wire gauges


The factor in the resistance which takes into account the nature of
the material is the resistivity . Although it is temperature dependent,
it can be used at a given temperature to calculate the resistance of a
wire of given geometry.




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