An unknown resistance wire in the left gap of a meter bridge balances a 10 resistance in the right gap at a point that divides the bridge wire in a ratio 3:2 . If the length of this unknown resistance wire is 1.5 m , what is its resistance per unit length? (Bridge wire is uniform)

Step-by-step solution

Let the unknown resistance in the left gap be R and the resistance in the right gap be S = 10 . At the balance point of the meter bridge, the ratio of resistances is equal to the ratio of the lengths of the bridge wire segments: R S = l₁ l₂ Given that the balance point divides the bridge wire in the ratio 3:2 , we have: R 10 = 3 2 R = 10 3 2 = 15 The length of the unknown resistance wire is L = 1.5 m . The resistance per unit length of the wire is: R L = 15 1.5 = 10.0 / m Answer: 10.0 / m