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In figure, key K is closed at t = 0. After a long time, the potential difference between A and B is zero, the value of R will be
[ $r_{1} = r_{2} = 1 Ω, E_{1} = 3 V a n d E_{2} = 7 V, C = 2 μ F, L = 4 m H$ where r₁ and r₂ are the internal resistances of cells E₁ and E₂ respectively].

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$\frac{2}{3} Ω$

$\frac{4}{9} Ω$

$\frac{4}{3} Ω$

$4 Ω$

answer is B.

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Detailed Solution

$E_{i} - i r_{1} = 0 \Rightarrow i = \frac{E_{1}}{r_{1}} = \frac{3}{1} = 3 Ω$

$i = \frac{10}{3 R + 2}, \frac{10}{3 R + 2} = 3, R = \frac{4}{9} Ω$

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