Electrical resistance questions

[wangdang]

Hi all,

I have a few questions on the factors that affect electrical resistance.
First off, here is my definition of electrical resistance: "The electrical resistance of a wire refers to the measure of the wire’s “opposition” to the free flow of electricity. "

Now, I would like to know how the LENGTH of a wire affects the level of electrical resistance. I understand that there is a greater distance for the current to travel, and therefore it would encounter a "greater overall" resistance, however I am looking for something more definitive. What exactly causes this increase in resistance? I have read about collisions but no websites have elaborated any further from just saying "there are more collisions".

I would also like to know how the TEMPERATURE of a wire affects resistance. Again, I have read about collisions but I would prefer to have an elaboration of that theory if possible. Also, I understand that an increase in temperature would increase the rate of vibrations of the atoms in the wire, but would it also increase the rate of vibrations for the moving charge particles? This would therefore increase the number of collisions between the moving charged particles and the object, thus resistance is increased?

Lastly, I would like to know how ELECTRICAL RESISTIVITY (the material composition of an object) affects resistance. I think this has something to do with the chemical composition of the material. Could someone explain it in reference to the atomic nature of the object (no. of valence electrons etc.), if that is the correct answer?

I am asking this from a year 11 level of knowledge, so please answer accordingly.
Thank you for your help guys.

P.S. If you could post any links to go with your answers, that would be appreciated.

 

[Andrew Mason]

Wikipedia has a good overview of resistance.

The reason resistance is directly proportional to length and inversely proportional to area is due to geometry more than the nature of the material in the resistor/conductor.

Given that a conductor of length L has a resistance R, if a voltage V is applied across it, a current I = V/R will flow. Now I add another identical conductor joined end to end in series with it and apply the same voltage drop across the two. By symmetry the voltage from one end to the point in the middle where the two conductors are joined has to be the same (same current through each, same resistance so the voltage drop over each has to be V/2). This means the current is halved so resistance doubles. Conclusion: resistance has to be proportional to length.

Do a similar exercise to see that if one puts two of these conductors of length L in parallel (doubling the cross-sectional area), the current doubles. So that resistance is inversely proportional to area.

AM

 

[wangdang]

Hi Andrew,
Thanks for the reply.
I am having some difficulty deriving the equation R = pL/A, which relates length, resistivity and cross sectional area to resistance. I have established that:
R α L
R α p (rho)
R α 1/A
What steps do I need to take from there, to prove (or show) that R = pL/A?

 

[Andrew Mason]

Hi Andrew,
Thanks for the reply.
I am having some difficulty deriving the equation R = pL/A, which relates length, resistivity and cross sectional area to resistance. I have established that:
R α L
R α p (rho)
R α 1/A
What steps do I need to take from there, to prove (or show) that R = pL/A?

None. If $R \propto L \text{ and } R \propto 1/A$ then:

$$R = k(\frac{L}{A})$$

where k = RA/L

We just call that constant of proportionality the conductor's "resistivity", $\rho$.

AM