Question

The torque of an ammeter varies as the square of the current through it. If a current of 5 A produces a deflection of 90, what deflection will occur for a current of 3 A when the instrument is (i) spring-controlled and (ii) gravity-controlled

Answer 1

Since deflecting torque varies as (current)2, we have Td ∝ I2

For spring control, Tc ∝ θ

∴ θ ∝ I2

For gravity control, Tc ∝ sinθ

∴ sinθ ∝ I2

(i) For spring control 90 ∝ 52 and θ ∝ 32 ; θ = 90° × 32/52 = 32.4

(ii) For gravity control sin 90 ∝ 52 and sinθ ∝ 32

sinθ = 9/25 = 0.36; θ = sin−1 (0.36) = 21.1.