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  4. Two cells of same emf but different internal resistances r 1 and r 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

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Q. Two cells of same emf but different internal resistances $r _{1}$ and $r _{2}$ 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 MainJEE Main 2022Current Electricity

Solution:

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