Question

A moving iron ammeter has constant rate of change of inductance with respect to deflection equal to $3\mu H/degree.$ The control torque is provided by spring having spring constant equal to $4\times {10}^{-7}N-m/degree.$ If the maximum deflection of pointer is 120°, then current corresponding to this maximum deflection will be _______A.

• A. 5.66

Answer 1

The correct option is A 5.66
Given,
$\text{Rate of change of inductance w.r.t. deflection}=3\mu H/degree$

Spring constant,
$K=4\times {10}^{-7}N-m/degree$

The deflection torque,
$T_d=\frac{1}{2}{I}^2\frac{dL}{d\theta }$

Controlling torque,
$T_c=K\theta =4\times {10}^{-7}\times {120}^o$

At steady state,

$T_d=T_c$

$4\times {10}^{-7}\times {120}^o=\frac{1}{2}\times I^2\times 3\times {10}^{-6}$

$I^2=\frac{2\times 4\times {10}^{-7}\times {120}^o}{3\times {10}^{-6}}$

$I^2=320\times {10}^{-1}=32$

$I=5.66A$