# Finding Resistvity

1. Nov 14, 2008

### atwong713

1. The problem statement, all variables and given/known data
calculate the resistivity of the germanium sample
setup below given the resistance and the dimensions
http://img25.imagevenue.com/img.php?image=91205_lab5_122_1170lo.JPG

2. Relevant equations
Resistivity=(resistance*Length)/(Area)

3. The attempt at a solution
Ok so I know how to find the resistivity of the setup if the wires were not on the corners of the sample, but since it is on the corner i know that i have to use an integral, so i have to use an integral right?

then dResistivity=(Resistance*dx)/A
putting the sample on a coordinate system
and after finding the value of y in terms of x
A = Thickness*(sqrt(50)-2x)
is this right so far??
i tried to do this but i keep getting a resistivity that is off from the resistivity of germanium

Last edited: Nov 14, 2008
2. Nov 14, 2008

### LowlyPion

And what is the set-up again?

3. Nov 14, 2008

### LowlyPion

What is the minimum contact cross section at the corner?

As that approaches 0, the resistivity approaches infinity doesn't it?

4. Nov 14, 2008

### atwong713

lol what do you mean?

5. Nov 14, 2008

### LowlyPion

When area approaches 0 ...

6. Nov 15, 2008

### atwong713

ok so there is an infinite resistivity when the area approaches zero do you have any hints on what to do next and how to set up the integral...I'm still kind of lost...do i integrate this from the middle of the square to the corner because of symmetry?

7. Nov 15, 2008

### LowlyPion

Are you sure your equation for resistivity is correct is my point.

http://en.wikipedia.org/wiki/Resistivity

8. Nov 15, 2008

### atwong713

ooo whoops i wrote the equation down wrong
i was suppose to do
dR=(resistivity*dx)/A
then integrate right? or do i use
dResistivity=(Resistance*A)/dx?

ok so i did it with the
dR=(resistivity*dx)/A
but i got ln(0) so it approaches -inf??

Last edited: Nov 15, 2008
9. Nov 15, 2008

### LowlyPion

What is it you are trying to calculate?

The resistivity?

Or the resistance?

10. Nov 15, 2008

### atwong713

im given the resistance of 2755Ohms at 300K
and i'm trying to find the resistivity.
so i'm guessing since i have the resistance i integrate all the resistances since they are in series so they just add?

this is what ive done so far
http://img226.imagevenue.com/img.php?image=91044_lab51_122_395lo.jpg

Last edited: Nov 15, 2008
11. Nov 15, 2008

### LowlyPion

Where did this come from?

Maybe if you gave a complete statement of the problem it would be a little easier?

12. Nov 15, 2008

### atwong713

o i'm sorry i shouldve been more specific i actually measured this in a lab and this is one of the questions for my lab report
so i measured the resistance of the germanium at different temperatures and now i'm just trying to find the resistivity given the setup i posted ealier
the dimensions of the sample is also on my first post...the only problem now is that i'm not sure how to setup the integral for finding this resistivity

13. Nov 17, 2008

### atwong713

ok for my end result i calculated a resistivity of .256(Ohm meters) using a resistance of 2755Ohms but the accepted value is .46 so am i doing this correct?