Two cells of the same EMF E but different internal resistances r _...

In this question we have to find the Terminal potential difference of second cell, we are given the internal resistances of both the cells and an external resistance. Applying the following expression:-

$V = E - i{r}_{2}$

$⇒ 0 = E - i{r}_{2}$

Applying the expression of current

$0 = E - \left(\dfrac{2E}{{r}_{1} + {r}_{2} + R}\right) \cdot {r}_{2}$

$⇒ R = {r}_{2} - {r}_{1}$