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In the arrangement shown in the figure when the switch $S_{2}$ is open, the galvanometer shows no deflection for l = L/2. When the switch $S_{2}$ is closed, the galvanometer shows no deflection for l = $\frac{5}{12} L$ . The internal resistance (r) of 6 V cell, and the emf E of the other battery are respectively

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3 $Ω$ , 8 V

2 $Ω$ , 12 V

3 $Ω$ , 12 V

2 $Ω$ , 24 V

answer is B.

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Detailed Solution

When $S_{2}$ is open, l= L/2
$∴ E = (\frac{6 V}{L / 2}) L = 12 V$
when $S_{2}$ is closed
$V_{10} = (\frac{12}{L}) \times \frac{5}{12} L = 5 V$
$But, V_{10} = 10 \times (\frac{6}{10 + r})$
$10 \times (\frac{6}{10 + r}) = 5 \Rightarrow r = 2 Ω$

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