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 \((ii)\)

\(\frac{E}{r_{2}}=\frac{2 E}{R+r_{1}+r_{2}}\)

\(\Rightarrow R=r_{2}-r_{1}\)