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derive the expression for conductivity in terms of resistivity using ohms law
![question image](http://images.topperlearning.com/topper/new-ate/top_mob169863852113650129339dcd97a6-2d24-4ce0-b556-350026522027.jpg)
Asked by yuvarajgududuru | 30 Oct, 2023, 09:32: AM
If R is resistance of conductor , V is volatge across conductors when current I is passing through it, then by Ohm's law
![begin mathsize 14px style R space equals space V over I end style](https://images.topperlearning.com/topper/tinymce/cache/4a1e1cb7c3b931e78b1638b75bd7de7a.png)
Resistance in terms of resistivity ρ is
![begin mathsize 14px style R space equals space rho space cross times L over A end style](https://images.topperlearning.com/topper/tinymce/cache/d2096b3bcdd4bdffc6eec5738b808dc4.png)
where L is length of conductor and A is area of cross section.
From (1) and (2) , we have
![begin mathsize 14px style rho space cross times space L over A space equals space V over I end style](https://images.topperlearning.com/topper/tinymce/cache/6fd62e350afa9e9c78318f887cc674fc.png)
![begin mathsize 14px style rho space equals space A over L cross times V over I end style](https://images.topperlearning.com/topper/tinymce/cache/0ea3e9e6c00a23df9c0316bbf521bb41.png)
Conductivity σ is reciprocal of resistivity , hence we get from above expression as
![begin mathsize 14px style sigma space equals space L over A space cross times I over V end style](https://images.topperlearning.com/topper/tinymce/cache/6962c5ff09fe161511e86e79c456fbd9.png)
From above expression conductivity of material of conductor can be determined by applying a voltage V across conductor ,
by measurring current I pass through it and from the known values of length L and cross section area A .
Answered by Thiyagarajan K | 30 Oct, 2023, 10:53: AM
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