\(\therefore E=K l\)

Here \(\mathrm{K}\) is potential gradient.

If the cell is short circuited by resistance \('R'\)

Let balancing length obtained be \(l'\) then

\({V=k l^{\prime}}\)

\({r=\left(\frac{E-V}{V}\right) R}\)

\(\Rightarrow \quad V=E-V\)  \([\because r=R \text { given }]\)

\(\Rightarrow \quad 2 V=E\)

or, \(\quad 2 K l^{\prime}=K l\)

\(\therefore \quad r=\frac{l}{2}\)