Question

a cooper wire of resistance r_{0 is stretched till its length is increased to n times of its original length.what will be its new resistance?}

Answer 1

$$\begin{gathered} letthelengthofwireislanditsresis\tan ceis{r}_0 \\ nowR=\rho \frac{l}{A},Where\rho =restivity,l=length,a=area \\ nowaccordingtoquestion: \\ {r}_0=\rho \frac{l}{A} \\ nowitweincreasethelengthtontimesthen \\ volumeofwiremustbecons\tan t \\ a\times l=A_{NEW}\times nl \\ {A}_{NEW}=\frac{a\times l}{nl}=\frac{a}{n}.....................1> \\ newresis\tan ce \\ R=\rho \frac{nl}{A_{new}}=\rho \frac{nl}{{\displaystyle \frac{a}{n}}}=\rho \frac{n^{2}l}{{\displaystyle a}}=n^2(\rho \frac{l}{A})=n^2{r}_0 \\ hencenewresis\tan ce\left(R\right)=n^2{r}_0. \end{gathered}$$