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When the length of a copper wire is incr...

When the length of a copper wire is increased by 0.1%, calculate the percentage change in its resistance.

A

`0.2%`

B

`2%`

C

`3%`

D

`0.4%`

Text Solution

Verified by Experts

The correct Answer is:
A
Volume of copper remains constant at V.
`thereforeR=(pL)/(A)=(pL)/(V//L)=p/(V)L^(2)orR=(p/(V)L^(2))`
Take log and differentiate.
`"log"R="log"(p/(V))+2"log"Lor(dR)/(R)=0+2(dL)/(L)or(dR)/(R)xx100=2(dL)/(L)xx100`
or % change in `R=2xx0.1/(100)xx100=0.2` `therefore` % change in R = 0.2%
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