The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be..... \(\%\).

\(\ell^{\prime} A =\ell A\)

\(2 \ell A ^{\prime}=\ell A\)

\(A ^{\prime}=\frac{ A }{2}\)

\(R =\rho \frac{\ell}{ A } \ldots\,\, (i)\)

\(\ell^{\prime}=2 \ell\)

\(A ^{\prime}=\frac{ A }{2}\)

\(R ^{\prime}=\frac{\rho \ell^{\prime}}{ A }=\frac{\rho 2 \ell}{\frac{ A }{2}}\)

\(R ^{\prime}=\frac{4 \rho \ell}{ A }\)

\(R ^{\prime}=4 R\) from equation \((i)\)

\(\%\) increase in resistance

\(=\frac{ R ^{\prime}- R }{ R } \times 100=\frac{4 R - R }{ R } \times 100\)

\(=300 \%\)