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 for same settings will be at
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Question

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 for same settings will be at

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G1 Physics · Accepted Answer

Initially: X/25 = r l₁/(r l₂) where, l₁ = 40 cm, l₂ = 60 cm After replacing the wire, resistance per unit length becomes 2r: X/25 = 2r l'₁/(2r l'₂) The factor 2r cancels, so the balance condition is unchanged. Hence, l'₁ = 40 cm