91Ó°ÊÓ

$$\begin{gathered} L=\text{10km} \\ \mathrm{Î\pm }=13\frac{\text{Ω}}{\text{km}} \\ R\text{'}+R=100,\text{whenmeasuredfromeastend.} \\ R\text{'}+R=200\text{,whenmeasuredfromwestend.} \end{gathered}$$

Write two equations forthe total resistance when measured from east end and west end. Solving them will give the values of x and R.

Formulae are as follow:

$R=R\text{'}+R$

Where, R is resistance.

The total resistance when measured from east end is,

$$\begin{gathered} R_e=R\text{'}+R \\ {R}_e=2\mathrm{Î\pm }(L−x)+R \\ 100=2\left(13\right)(10−x)+R \\ 26x−R=160………………………………………………………………………………1) \end{gathered}$$

The total resistance when measured from west end is,

$$\begin{gathered} R_w=R\text{'}+R \\ {R}_w=2\mathrm{Î\pm }x+R \\ 200=2(13×x)+R \\ 26x+R=200………………………………………………………………………………2) \end{gathered}$$

Adding 1) and 2), we get

$$\begin{gathered} 52x=360 \\ ∴x=\text{6.9km} \end{gathered}$$

Hence, the value of x is $\text{6.9km}$

Inserting the value of x in equation 1) gives,

$$\begin{gathered} R=26\left(6.92\right)−160 \\ R=19.92~20\text{Ω} \end{gathered}$$

Hence, the value of R is $20\mathrm{Î\copyright }.$

Therefore, find the resistance of the short from the total resistance of the wire from both the ends.