1 Road Safety And Automobile Association Patrol In Great Britain

DIMENTIONS OF CONDUCTORS AND RESISTANCE

The electrical resistance of a conductor depends upon its shape. A cube of copper with sides 10mm x 10mm x 10mm has a resistance of about 0.000 002Q. If the copper in this cube were drawn out into a thin wire 100m long the cross-section would decrease from 10mm x 10mm to 0.1mm x 0.1mm. The resistance from the face at one end to the face at the other end, 100m away, would be about 200Q.

Therefore, changing the shape of the piece of copper has changed its resistance by 100 million times.
The resistance of a conductor depends upon its length, its cross-section area, and the material of which It Is made.

The constant depends upon the material that the conductor is made from. The constant for copper is different from the constant for aluminum.

The equation summarizes the following:
a) The resistance of a conductor is proportional to its length (if the cross-section area remains the same). If the length of a conductor is doubled, keeping the cross-section the same, the resistance is doubled. If the length is halved, the resistance is halved.
b) The resistance of a conductor is inversely proportional to the cross-section area {if the length remains the same). If the cross-section area is doubled, keeping the length the same, the resistance is halved. If the cross-section area is halved, the resistance is doubled.
Temperature and resistance
Figure 1 shows that the copper conductor of 1mm² cross-section and 1km length has a resistance of about 18Q at room temperature. At the temperature of boiling water, the resistance of this same conductor would be about 24£i. That is, it increases by about 6Q. As a rough guide, the resistance of a copper conductor increases by about 1/3 of its value at room temperature for every 70K rise in temperature. If the temperature drops, then the resistance of a copper conductor decreases by about 1/3 of its value at room temperature for every 70K drop in temperature.
This has to be taken very carefully into account by engineers. Electrical machinery is made and assembled in workshops at room temperature, but when it is working some of its parts may be well above room temperature.

Topic # 8