a
$I=\frac{2 E }{R+I_{1}+I_{2}} \ldots \ldots( i )$
But $V _{ A }- V _{ B }= E - I _{2}=0$
$\Rightarrow I =\frac{ E }{ I _{2}} \quad \ldots \text { $(ii)$}$
Comparing values of $I$ from $(i)$ and $(ii)$
$\frac{E}{r_{2}}=\frac{2 E}{R+r_{1}+r_{2}}$
$\Rightarrow R=r_{2}-r_{1}$
