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 90º, 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 T_d ∝ I²

For spring control, T_c ∝ θ 

∴ θ ∝ I² 

For gravity control, T_c ∝ sinθ

∴ sinθ ∝ I²

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

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

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