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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

15 $Ω$

b

10 $Ω$

c

8 $Ω$

d

6 $Ω$

answer is B.

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Detailed Solution

The balanced Wheatstone bridge is shown in fig

Question Image

Now, $\frac{R_{AJ}}{R_{JB}} = \frac{12 Ω}{X}$
The balance on the wire is obtained when jockey is at a distance of 60 cm from A. The resistance R_AJ 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
$∴ \frac{0 \cdot 6 ρ}{0 \cdot 4 ρ} = \frac{12 Ω}{X} or X = 8 Ω$

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