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 $r_2\, (r_1 >\, r_2)$ respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of $R$ is :-

• A. $r_1 + r_2$
• B. $r_1 - r_2$
• C. $\frac{r_1 + r_2}{2}$
• D. $\frac{r_1 - r_2}{2}$

Answer 1

Answer: (B)

Current in the circuit
$I=\frac{2 E}{R+r_{1}+r_{2}}$
$\therefore$ Potential difference across first cell
$V = E - I _{ r _{1}}= E -\frac{2 Er _{1}}{\left( R + r _{1}+ r _{2}\right)}=0$
On solving we get, $ R =\left( r _{1}- r _{2}\right)$