Two resistances are connected in the two gaps of a meter bridge. The balancing point is obtained at 20 ~cm . When a resistance of 15 is connected in series with the smaller resistance of the two, the balancing point shifts to 40 ~cm . The value of smaller resistance is

Step-by-step solution

aligned & L =20 ~cm ; L ^ =40 ~cm & Using R ₁ R ₂ = L 100- L = 20 100-20 = 20 80 & R ₂=4 R ₁ & R ₁^ R ₂^ = L ^ 100- L ^ = 40 100-40 = 40 60 = 2 3 & Here R ₁^ = R ₁+15 and R ₂ ^ = R ₂=4 R ₁ & R ₁+15 4 R ₁ = 2 3 & 3 R ₁+45=8 R ₁ & R ₁=9 Smaller resistance aligned