Two cells of same emf but different internal resistances $I_{1}$ and $I_{2}$ are connected in series with a resistance $R$. The value of resistance $R$, for which the potential difference across second cell is zero, is
JEE MAIN 2022, Medium
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$I=\frac{2 E }{R+I_{1}+I_{2}} \ldots \ldots( i )$
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 $(ii)$
$\frac{E}{r_{2}}=\frac{2 E}{R+r_{1}+r_{2}}$
$\Rightarrow R=r_{2}-r_{1}$
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