Question on relationship between drift velocity and resistance

[arjose]

Is there a relationship (or equation) between a charge carrier's drift velocity through a conducting material and that material's resistance? I'm trying to reconcile the idea that drift speeds are bigger when cross sections are smaller and the idea that resistance is bigger when cross sections are smaller. How can the drift speed be faster in smaller cross sections when resistance is bigger? I have this idea that drift speeds are proportional to current and inversely proportional to resistance. Am I right?

 

[ardie]

it is not quite appropriate to think of cross sections of particles in a material to be directly related to the resistance. the number density will come into play and without a clear knowledge of the composition, it will not be possible to formulate resistance. Instead one thinks of the average time it takes for each electron to collide, and this is related to the drift velocity in the free electron gas model. More commonly, one defines a quantity called the electron mobility, and this is related directly to the conductivity, hence inversely related to resistance of the material. here's more information on electron mobility:
http://en.wikipedia.org/wiki/Electron_mobility