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

Question

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

Infinity Learn · Accepted Answer

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 ×  $$5L12=5$$  ×  $$1212$$ $$=$$  $$5V$$⇒   $$6$$−$$I1r$$ $$=5$$  ⇒  $$6$$−$$510$$ $$r=5$$  ⇒  $$r=2$$Ω

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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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