resistivity measurements of a circular shaped sample

brk

Hai,
I am doing my masters degree in physics. can somebody help me in which formula to use for calculating resistivity of a sample of circular shape using two probe measurements, which should include thickness and correction factor also.
Thank You!!!

Simon Bridge

Welcome to PF;
You should be able to get the resistivity from a measurement of the DC resistance across the sample and it's geometry. Which direction you take the resistance measurement depends on the specifics of your samples shape. "circular shape" is a little vague.

brk

thanks for the reply...
I measured the dc resistance already,but how to calculate the resistivity for a circular sample. Using two probe method.

Studiot

Circular is a 2 dimensional shape. You have lost one dimension.

It is usual to choose the measurement sample so that it is long compared to its cross sectional area (ie along a length of wire) so that the effect of the spread of current may be ignored.

If you are measuring across a disk or ball shaped object then you will have to set up and solve the Coulomb-Bousinesq equations, using your dimensions as boundary conditions. Hertz solved these in about 1885.

However it is a three dimensional problem so you need to be clear as to the geometry.

Simon Bridge

I was gonna say - yeah ... "circular volume" is sometimes used to describe a flat cylinder though - like a coin is "a circle" in common language, right?

Still, I did try to prompt for this:... maybe that should have been an explicit question. OK. What is the 3D geometry of your sample?

Otherwise the best anyone can do is describe the 2-probe method in general.

brk

i understood what you are trying to convey!!!
it is circular disk shaped sample of thickness of 1mm or so. The resistivity of the sample is very high, so we preferred to measure using two probe method. There are formulas for vanderpauw, collinear four probe configurations to calculate the resistivity from the measured voltage. Similarly i need a formula for two probe configuration to calculate the resistivity of circular disk shaped sample.

Studiot

You still didn't answer the question about the geometry.

brk

it is circular pellet of thickness 0.6mm and diameter 13mm.