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)

$r_1 - r_2$

Answer 2

According to question $E - Ir _{1}=0$ & $I =\frac{ E + E }{ r _{1}+ r _{2}+ R }$ $\therefore \frac{ E }{ r _{1}}=\frac{2 E }{ r _{1}+ r _{2}+ R }$ $\Rightarrow r _{1}+ r _{2}+ R =2 r _{1}$ $\Rightarrow R = r _{1}- r _{2}$