find the percent change in resistance as seen in picture
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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,
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.
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option c is your answer. hope this helps you
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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.
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