Question

An electric wire is stretched to increase its length by 25%. By what % will the resistance be increased and what will be increase in its resistivity?
Class 10th Physics​

Answer 1

Answer:

First thing first, resistivity is the intrinsic property of a material which doesn't changes (considering at normal conditions).

The relationship between Resistance R and the Resistivity ρ is

R=ρ×l/A  

Where  l  is the length of the wire and  A  is its cross sectional area.

Now, taking the logarith and differentiating,

We have

ΔR/R=Δl/l−ΔA/A  

Since ρ  is constant so it will be eliminated.

Considering no change in the cross sectional area, the equation remains :  ΔR/R=Δl/l  

Multiply by 100 results in percentage error.

(ΔR/R)×100=(Δl/l)×100  

Given is percentage increase in length is 25%

So,  (ΔR/R)×100=25  

Or percentage increase in resistivity is 25%.

P.s the cross sectional area is considered unchanged here as no information is given about that. However, this is not practical amd it does change on extension of wire.

Explanation: