The resistance per centimeter of a meter bridge wire is r, with resistance in left gap. Balancing length from left end is at 40 cm with resistance in right gap. Now the wire is replaced by another wire of resistance per centimeter. The new balancing le

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Solution

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 $2 r$ resistance per centimeter. The new balancing length for same settings will be at [2024]

1 20 cm

2 10 cm

3 80 cm

4 40 cm

Ans.
(4)

$\frac{25}{r ℓ_{2}} = \frac{X}{r ℓ_{1}}$ ...(i)

$\frac{25}{2 r ℓ'_{2}} = \frac{X}{2 r ℓ'_{1}}$ ...(ii)

From (i) and (ii) $ℓ'_{2} = ℓ_{2} = 40 c m$

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