Resistance and Ohm's Law Problem

[clairez93]

Homework Statement

A solid cube of silver (density = 10.5 g/cm^3) has a mass of 90.0 g. (a) What is the resistance between the opposite faces of the cube? (b) If there is one conduction electron for each silver atom, what is the average drift speed of electrons when a potential difference of 1.00 x 10^-5 V is applied to opposite faces? (The atomic number of silver is 47, and its molar mass is 107.87 g/mol)

Homework Equations

(listing all the equations given in the section this problem is relevant to)

J = $$\sigma$$E
J = nqv$$_{d}$$
R = $$\ell$$ / $$\sigma$$A = $$\Delta$$V / I
$$\rho$$ = 1 / $$\sigma$$
R = $$\rho$$$$\ell$$ / A

The Attempt at a Solution

I am completely clueless, at how to start. I think I'll have to use one of the R formulas somehow, but there seems to be too many unknown variables if I try to use any of those. Could someone help me get started?

The book's answer is (a) 777 n$$\Omega$$ (b) 3.28 $$\mu$$m/S

 

[alphysicist]

Hi clairez93,


About there seeming to be too many unknowns, I would guess that they want you to look up the resistivity of silver; you should have a table of those values in your book. Once you have that, the other values in the problem will be all you need to work with.

 

[clairez93]

R = $$\rho$$$$\ell$$ / A
I am thinking this is the one I will need to use. For $$\rho$$ I think I will need to look up resistivity. For ell and A, I will need to use the density and mass to get a volume number, I believe, correct?

I'm not sure how to figure out prat b for a drift speed though. I don't see a formula in the section the problem is supposed to belong to for a drift speed. Is there a certain formula I should be using?

 

[alphysicist]

R = $$\rho$$$$\ell$$ / A
I am thinking this is the one I will need to use. For $$\rho$$ I think I will need to look up resistivity. For ell and A, I will need to use the density and mass to get a volume number, I believe, correct?

That's sounds right.

I'm not sure how to figure out prat b for a drift speed though. I don't see a formula in the section the problem is supposed to belong to for a drift speed. Is there a certain formula I should be using?

One of the formulas you listed in the relevant equations has the drift speed in it. There is a very similar formula that has the current instead of the current density that might be a bit more straightforward.

 

[Kabbotta]

Part A:

R = $$\rho$$r / A

Part B:

J = I / A = nq$$v_{d}$$

Hope this is still useful.