Question

Inductance of moving iron instrument is given by L=(12+6ø-ø2)µH Where ø is the Deflection in radians from zero position. The spring constant is 12*10-6 Nm/Rad. calculate the Deflection for current of 8 amp.

Answer 1

For the given current, the deflection is

$$\theta=\frac12 \frac{I^2}{k}\frac{\text dL}{\text d\theta},\\\space\\ \theta=\frac12 \frac{I^2}{k}\frac{\text d(12+6\theta-\theta^2)}{\text d\theta},\\\space\\ \theta=\frac12 \frac{I^2}{k}(6-2\theta),\\\space\\ \theta=3\text{ rad}.$$