Calculate Resistivity of a Rod

[harts]

Homework Statement

A uniform metallic rod, with a cross-sectional area of 1.83 cm2
and a length of 7.08 m, contains 6.24E28 conduction electrons per cubic meter of material, which have a mean collision time of 20.2 femtoseconds.

(a) Determine the resistivity of the rod.

When the rod experiences a potential difference of 2.52 mV from end to end, determine
(b) the drift velocity of the electrons and
(c) the current density in the rod.

Homework Equations

R = ρl/A
J = ΔV/(ρl)
v_d = I/(neA) (n being the number of mobile charge carriers per unit volume, e is electron charge)

The Attempt at a Solution

So I know exactly how to do b and c, those are a piece of cake. Unfortunately, to actually answer those parts I need the answer from part a which I have no idea how to do.

I started by saying ρ=AR/l, but then I realized I don't have R directly given to me. All of the methods I thought of to get R involved needing information I wouldn't get till later steps (using Ohm's law and finding R from I_avg = nqv_dA and known value of V, don't have v_d; using ρ=E/J, J being current density which I also don't have yet.

I can't find anything in my book. I would guess that materials with higher resistivities have more frequent collisions (so higher mean collision times); more collisions, more resisting going on. As for conduction electron intuition, I'm not really sure. Any help?? I know the answer ranges from 1.5E-08 to 3.00E-08, so I even got desperate and tried multiplying values together to see if I could get anything within that order of magnitude.

 

[anathema]

Hi there! The resistivity of a material is a measure of its resistance to electrical current flow. In order to calculate the resistivity of the rod, we can use the resistivity formula that you have mentioned: R = ρl/A. However, in order to use this formula, we need to know the resistance of the rod, which is given by Ohm's law (R = V/I). Since we have the potential difference (V) and the length (l) and cross-sectional area (A) of the rod, we can rearrange Ohm's law to find the resistance (R). Once we have the resistance, we can substitute it into the resistivity formula to find the resistivity (ρ).

Remember, resistivity is a property of the material, so it will not change with different potential differences or current densities. It is a constant value for a given material.

I hope this helps! Let me know if you have any further questions. Good luck with your calculations!