Two cells, having the same e.m.f. are connected in series through an external resistance $R$. Cells

Question

Two cells, having the same e.m.f. are connected in series through an external resistance $R$. Cells have internal resistances $r_{1}$ and $r_{2}\left(r_{1}>r_{2}ight)$ respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of $R$ is\

Professor PC Thomas Classes · Answer

(b) : Current in the circuit,\ $i=\frac{2 E}{\left(r_{1}+r_{2}+Right)}$.\ As per question, $E-i r_{1}=0$\ $i=\frac{E}{r_{1}}$ or, $\frac{2 E}{r_{1}+r_{2}+R}=\frac{E}{r_{1}}$ or, $2 r_{1}=r_{1}+r_{2}+R$ or, $R=r_{1}-r_{2}$\