Answer with Explanation:
Let r be the resistance of short piece of copper wire.
Resistance of copper wire=R=![13\Omega](https://tex.z-dn.net/?f=13%5COmega)
Resistance is directly proportional to length.
If a wire has greater resistance then,the wire will be greater in length.
Therefore,resistance of long piece of wire=7r
Total resistance of copper wire=Sum of resistance of two piece of wires
![r+7r=13](https://tex.z-dn.net/?f=r%2B7r%3D13)
![8r=13](https://tex.z-dn.net/?f=8r%3D13)
ohm
Resistance of long piece of wire=![7\times\frac{13}{8}=\frac{91}{8}\Omega](https://tex.z-dn.net/?f=7%5Ctimes%5Cfrac%7B13%7D%7B8%7D%3D%5Cfrac%7B91%7D%7B8%7D%5COmega)
Resistance of short piece of wire =![\frac{13}{8}\Omega](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B8%7D%5COmega)
Resistivity of wire and cross section area of wire remains same .
Let L be the total length of wire and L' be the length of short piece of wire.
We know that
=![\frac{\rho}{A}L=KL](https://tex.z-dn.net/?f=%5Cfrac%7B%5Crho%7D%7BA%7DL%3DKL)
![\frac{R}{L}=K](https://tex.z-dn.net/?f=%5Cfrac%7BR%7D%7BL%7D%3DK)
Where K=
=Constant
Using the formula
![\frac{13}{L}=\frac{\frac{13}{8}}{L'}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7BL%7D%3D%5Cfrac%7B%5Cfrac%7B13%7D%7B8%7D%7D%7BL%27%7D)
![\frac{L'}{L}=\frac{13}{8}\times \frac{1}{13}=\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7BL%27%7D%7BL%7D%3D%5Cfrac%7B13%7D%7B8%7D%5Ctimes%20%5Cfrac%7B1%7D%7B13%7D%3D%5Cfrac%7B1%7D%7B8%7D)
![L'=\frac{L}{8}](https://tex.z-dn.net/?f=L%27%3D%5Cfrac%7BL%7D%7B8%7D)
Length of short piece of wire=L'=![\frac{L}{8}](https://tex.z-dn.net/?f=%5Cfrac%7BL%7D%7B8%7D)
Length of long piece of wire=![L-L'=L-\frac{L}{8}=\frac{8L-L}{8}=\frac{7}{8}L](https://tex.z-dn.net/?f=L-L%27%3DL-%5Cfrac%7BL%7D%7B8%7D%3D%5Cfrac%7B8L-L%7D%7B8%7D%3D%5Cfrac%7B7%7D%7B8%7DL)
% of length of short piece of wire=
%
The resistance of the short piece=![\frac{13}{8}\Omega](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B8%7D%5COmega)
The resistance of the long piece=![\frac{91}{8}\Omega](https://tex.z-dn.net/?f=%5Cfrac%7B91%7D%7B8%7D%5COmega)