c
(b) Let the voltage across any one cell is $V$, then
$V = E - ir = E - {r_1}\,\left( {\frac{{2E}}{{{r_1} + {r_2} + R}}} \right)$
But $V = 0$
$==>$ $E - \frac{{2E{r_1}}}{{{r_1} + {r_2} + R}} = 0$
$==>$ ${r_1} + {r_2} + R = 2{r_1}$
$==>$ $R = {r_1} - {r_2}$
