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derive the expression for conductivity in terms of resistivity using ohms law
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Asked by yuvarajgududuru | 30 Oct, 2023, 09:32: AM
answered-by-expert Expert Answer
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 ................................ (1)
 
Resistance in terms of resistivity ρ is
 
begin mathsize 14px style R space equals space rho space cross times L over A end style ..............................(2)
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
begin mathsize 14px style rho space equals space A over L cross times V over I end style
 
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  ..............................(3)
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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