A galvanometer of resistance 30 Ω is connected to a battery of emf 2 V with 1970 Ω resistance in series. A full-scale deflection of 20 divisions is obtained in the galvanometer. To reduce the deflection to 10 divisions, the resistance value (in ohm) in series required is

Step-by-step solution

i = V R e f f = V 1970 + 30 = 2 2000 = 1 × 10 - 3 A = 1 m A This current provides full scale deflection (i.e. 20 division) In order to limit the deflection 10 divisions, the resistances needed to connect can be obtained as θ = n i A B k ∴ θ 1 θ 2 = i 1 i 2 ∴ θ 1 : θ 2 = 2 ∴ i 1 : i 2 = 2:1 ∴ i 2 = i 1 2 = 1 × 10 - 3 2 = 5 × 10 - 4 m A ∴ i = V R e f f + R s ⇒ R s = V i - R e f f = 2 5 × 10 - 4 - 2000 = 2 5 × 10 4 - 2000 = 4 × 10 3 - 2000 = 2000 Ω ∴ The resistance of 1970 Ω is to be replaced by 1970 + 2000 = 3970 Ω