The resistances in the two gaps of a balanced meter bridge are 'X' and '3X' respectively. If the resistances are interchanged the balance point shifts by

Step-by-step solution

For a balanced meter bridge, the condition is R₁ R₂ = l 100 - l Initially, the resistances are X and 3X . Let the balancing length be l₁ . X 3X = l₁ 100 - l₁ 1 3 = l₁ 100 - l₁ 100 - l₁ = 3l₁ 4l₁ = 100 l₁ = 25 cm When the resistances are interchanged, the new resistances in the gaps are 3X and X . Let the new balancing length be l₂ . 3X X = l₂ 100 - l₂ 3 = l₂ 100 - l₂ 300 - 3l₂ = l₂ 4l₂ = 300 l₂ = 75 cm The shift in the balance point is l = l₂ - l₁ = 75 - 25 = 50 cm. Answer: 50 cm