To measure the internal resistance of a battery, potentiometer is used. For \(\mathrm{R}=10 \Omega\), the balance point is observed at \(\ell=500 \mathrm{~cm}\) and for \(\mathrm{R}=1 \Omega\) the balance point is observed at \(\ell=400 \mathrm{~cm}\). The internal resistance of the battery is approximately _______.

\(\therefore \mathrm{i} \times 10=\lambda \times 500=\varepsilon-\mathrm{ir}_{\mathrm{s}}\)

\(\Rightarrow 500 \lambda=\varepsilon-50 \lambda \mathrm{r}_{\mathrm{s}}\)

Also,

\(\mathrm{i}^{\prime} \times 1=\lambda \times 400=\varepsilon-\mathrm{i}^{\prime} \mathrm{r}_{\mathrm{s}}\)

\(\Rightarrow 400 \lambda=\varepsilon-400 \lambda \mathrm{r}_{\mathrm{s}}\)

\(\therefore 100 \lambda=350 \lambda \mathrm{r}_{\mathrm{s}} \Rightarrow \mathrm{r}_{\mathrm{s}}=\frac{10}{35} \approx 0.3 \Omega\)

Hence option \((4)\)