In a meter bridge experiment, two unknown resistances R₁ and R₂ are connected in the left and right gaps respectively. When the positions of R₁ and R₂ are interchanged, the balance point shifts by 40 cm . If the equivalent resistance of R₁ and R₂ connected in series is 100 and R₁ > R₂ , the value of R₁ is _____ .

Step-by-step solution

Let the initial balance point from the left end be l . Since R₁ > R₂ , the initial balance point l > 50 cm . The balance condition is: R₁ R₂ = l 100 - l When R₁ and R₂ are interchanged, the new balance point l' from the left end will be 100 - l . The shift in the balance point is given as 40 cm . l - (100 - l) = 40 2l - 100 = 40 2l = 140 l = 70 cm Now, substituting l = 70 cm in the balance condition: R₁ R₂ = 70 100 - 70 = 7 3 R₂ = 3 7 R₁ Given that the series combination R₁ + R₂ = 100 : R₁ + 3 7 R₁ = 100 10 7 R₁ =