A copper wire is stretched to make it `0.5%` longer. The percentage change in its electrical resistance if its volume remains unchanged is :

Options

A. 0.025
B. 0.005
C. 0.01
D. 0.02

Answer

C

Explanation

`R=(rho l)/A prop l/A`
If volume is constant `Al=` constant
`impliesR prop l^(2) prop 1/(A^(2))`
Now `(R_(2))/(R_(1))=((l_(2))/(l_(1)))^(2),l_(2)=l_(1)+0.5/100l_(1)`
`implies(R_(2))/(R_(1))=(1+0.5/100)^(2)(1+(2xx0.5)/100)=101/100implies(R_(2)-R_(1))/(R_(1)0=1/100 1%`