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Q.

The resistance per centimeter of a meter bridge wire is r, with $X Ω$ resistance in left gap. Balancing length from left end is at 40 cm with $25 Ω$ resistance in right gap. Now the wire is replaced by another wire of 2r resistance per centimeter. The new balancing length from left for same settings will be

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a

20 cm

b

80 cm

c

40 cm

d

10 cm

answer is B.

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Detailed Solution

$\frac{X}{R} = \frac{ℓ}{100 - ℓ}$
For same X and R balancing length will not change even though metre bridge wire resistance per unit length changes.

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The resistance per centimeter of a meter bridge wire is r, with XΩ resistance in left gap. Balancing length from left end is at 40 cm with 25Ω resistance in right gap. Now the wire is replaced by another wire of 2r resistance per centimeter. The new balancing length from left for same settings will be