Electricity Tutorial 4 - Resistivity

The resistance of a wire depends on three factors:

Resistivity is a property of the material.  It is defined as the resistance of a wire of the material of unit area and unit length.

The formula for resistivity is:

In physics code we write this as r = AR/l

  There are three bear traps

 Question 1

Constantan has a resistivity of 47 ´ 10-8 Wm.  How much of this wire is needed to make a 10 ohm resistor, if the diameter is 0.5 mm? 

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The reciprocal or inverse of resistivity is conductivity.  It has the physics code s, (“sigma”, a Greek letter ‘s’), and units Siemens per metre (S m-1).

Conductivity is given by the relationship:

Super-conduction

A super-conductor is a material that has zero resistance.  A current flows when there is no potential difference.  The piece of metal floating above the magnet shows that there must be a current flowing.

 

Picture from Wikimedia Commons. 

Authors: Julien Bobroff and Frederic Bouquet

 

For all metals the resistivity (hence resistance) decreases as they get colder.

 

For some metals like copper and silver, there is still a tiny bit of resistance left at very low temperatures. 

 

Very low temperatures have to be maintained, which is expensive.  Room temperature superconductivity has not been seen.

Super-conductivity is seen in:

 

All superconductors have a critical temperature above which the phenomenon stops.  The graph below shows the idea:

 

 

Above the boiling point of liquid nitrogen, 77 K (-196 oC), superconductivity can be observed in a few materials.  These are called high temperature superconductors.

 

Very large magnets such as those found in the large hadron collider have coils made of superconducting materials.  It is believed that the superconductivity will last 100 000 years, as long as the coils don’t go above their critical temperature.

 

The mechanism for super-conduction is complex, and cannot be explained in terms of electrons colliding with ions.

Question 2

Explain what happens when a super-conducting metal reaches its critical temperature.

Answer