A thin uniform wire AB of length $$1$$ m, and unknown resistance X and a resistance of $$12$$ Ω are connected by thick conducting strips as shown in fig. A battery and galvanometer are also connected as shown in the figure. It is found that no deflection takes place in the galvanometer when the sliding jockey touches the wire at a distance of $$60$$ cm from A. The unknown resistance X is

Question

A thin uniform wire AB of length $$1$$ m, and unknown resistance X and a resistance of $$12$$ Ω are connected by thick conducting strips as shown in fig. A battery and galvanometer are also connected as shown in the figure. It is found that no deflection takes place in the galvanometer when the sliding jockey touches the wire at a distance of $$60$$ cm from A. The unknown resistance X is

Infinity Learn · Accepted Answer

The balanced Wheatstone bridge is shown in fig Now, $$RAJRJB=12$$ΩXThe balance on the wire is obtained when jockey is at a distance of $$60$$ cm from A. The resistance RAJ is $$0.6$$ p where p is resistance per unit length of wire. The resistance of JB part of the wire $$is(1$$ $$-0.6)$$ p $$=$$ $$0.4p$$∴ $$0$$⋅$$6$$ρ$$0$$⋅$$4$$ρ$$=12$$ΩX  or  $$X=8$$Ω

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