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Q.

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

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a

6 Ω

b

8 Ω

c

10 Ω

d

15 Ω

answer is B.

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Detailed Solution

The balanced Wheatstone bridge is shown in fig Now, RAJRJB=12ΩXThe 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⋅6ρ0⋅4ρ=12ΩX  or  X=8Ω
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