[fay]

Hi! :)
I'm doing a GCSE coursework and could you please give me a very detailed explanation of how resistance is caused in a wire (constantan wire) as its length is increased;why the resistance increases.
Thank you so much
:-*

[sclark]

Metals conduct electricity because the atoms in them do not hold on to their electrons very well. This creates free electrons, carrying a negative charge to jump along the line of atoms in a wire.

The electrons move from a loosely held state on one atom to a 'hole' in the next. Not all atoms in a metal have available holes at all times. This means that electrons sometimes need to 'jump' full atoms. Resistance is caused when these electrons flowing towards the positive terminal have to 'jump' atoms.

If we double the length of a wire, the number of atoms in the wire doubles, so the number of jumps double. Therefore, twice the amount of energy is required: There are twice as many jumps if the wire is twice as long. Therefore, resistance is proportional to the length directly.

A thinner wire has less channels of electrons in the wire for current to flow, so the energy is not spread out as much, so the resistance will be higher: We see that if the area of the wire doubles, so does the number of possible routes for the current to flow down, therefore the energy is twice as spread out, so resistance might halve. This shows that resistance is proportional to 1/Area.

Under constant temperature conditions, the resistance of a wire is shown to be:

R = (rho)L/A

R is the resistance
Rho is the characteristic of the material, and is a measured quantity. Copper has a different rho than say, carbon.
L is the length of the wire
A is the effective cross sectional area of the wire.