In the arrangement shown in figure, when the switch S2 is open, the galvanometer shows no deflection for l=L2. When the switch S2 is closed, the galvanometer shows no deflection for l=5L12. The internal resistance (r) of 6 V cell, and the emf E of the other battery are respectively
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a
3 Ω, 8 V
b
2 Ω, 12 V
c
2 Ω, 24 V
d
3 Ω, 12 V
answer is B.
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Detailed Solution
When S2 open:Assume resistance of AB = RResistance of wire per unit length, x=RLI=ERNow for null point at l=L2ER × RL × L2=6E = 12 VV1=ER × RL × 5L12=5 × 1212 = 5V⇒ 6−I1r =5 ⇒ 6−510 r=5 ⇒ r=2Ω