Question

What is the conductivity of a conduit with a cross-sectional area of `0.60` `cm^2` and a length of `15` `cm`, given that its conductance `G` is `0.050` `ohm`?

Answer 1

The conductivity is `8000(Omega-m)^-1`.

Explanation:

#the reciprocal of resistivity is **conductivity**. #sigma=(1)/(rho)#. Here given conductance G is 0.050#mho`or 0.050`(ohm)^-1#, because the conductance is reciprocal of resistivity so as its units also. So I am considering that. So Resistance is #R=1//G# by substituting the given value we get #R=20ohm#.

Now the resistance R of a particular conductor is related to the resistivity `rho` of its material by
`R=(rhol)/(A) =>rho=(RA)/(l)`
Calculating with the given above analysis
`rho= (20ohmxx0.60cm^2)//(15cm) = 0.8ohm-cm`
`=>rho=8xx10^-3 ohm-m`.
Now substitute the resistivity value in above conductivity we get,
`sigma=(1)/(rho) = 8000(ohm-m)^1`.