An attraction type moving iron instrument works based on the principle of attraction of a magnetic material towards the coil.
Basic Structure
Suppose there is a coil. We connect this coil with an electric source. Whenever we inject current into the coil, the coil will become a magnet. Obviously, this magnet attracts any iron pieces nearby. The attraction force of the coil magnet depends on the value of the current flowing through the coil. By viewing the position of the magnetic piece, one can detect the intensity of the current in the coil.
In an attraction type moving iron instrument, we do the same. Here, we use a typically shaped iron disc attached with a hinge in front of a coil. We fix one pointer on the iron disc. When the disc rotates about the hinge, the pointer will also rotate.
The position of the pointer tip depends upon the angle of rotation of the iron disc.
Basic Principle of Attraction Type Moving Iron Instrument
Whenever current starts flowing through the coil, the coil will attract the iron piece towards it due to its magnetizing effect. As a result, the iron piece rotates and reaches an equilibrium angle. After a certain angle, the torque due to the weight of the iron piece will be in equilibrium with the torque due to the attraction of the magnetic field on the iron piece. Thereby, the pointer will stop at a certain angle.
This angle tells us the position of the pointer tip. Then we calibrate the position of the pointer tip according to the injected current to the coil. By reducing and increasing the current by known values, we can mark the pointer head at each occasion. In this way, we can prepare a scale for the measurement of current.
So when we supply an unknown current to the coil, the pointer will rotate due to the attraction force. It will fix at a certain position. From that position, we can read the actual current we are injecting into the coil.
That is the very basic working principle of an attraction type moving iron instrument.
Expression for Deflection
For the derivation of the deflection expression, we first need to consider a current I flowing through the coil of the instrument. Due to that current, the coil attracts the soft iron vane. As a result, the vane has an angular displacement of \(\theta\). As the alignment of the soft iron vane has been changed due to the magnetic attraction, there will be a change in the total inductance of the coil.
When there is a current I flowing through the coil, the coil stores energy in its magnetic field as \[W_m = \frac{1}{2}LI^2\] where, L is the inductance of the coil.
Work Done due to Deflection
The total work done for that angular movement will be \[W_{mech} = T_d \cdot d\theta\]Where \(T_d\) is the deflecting torque produced by the instrument. Now, due to this deflection of the vane, there will be a change in inductance of the coil, and we can say this change is dL. Because of that change in inductance of the coil, the change in stored magnetic energy will be\[dW_m = \frac{1}{2}I^2 \, dL\]Now, due to the rotation of the moving vane, there will be work done, which obviously equals the change in magnetic energy. So we can write\[T_d d\theta = \frac{1}{2}I^2 dL\]\[\Rightarrow T_d = \frac{1}{2}I^2 \frac{dL}{d\theta}\]This expression shows that the deflecting torque \(T_d\) is directly proportional to the square of the current.
Here, we have considered that the change of inductance per degree change in angular position is constant for that coil.
Controlling Torque
Now, \(\theta\) is the total angular displacement due to current I in the coil. Then we can write the expression of controlling torque as\[T_c = K\theta\]Where K is the constant of restoring force. When we use a spring-controlled instrument, K will represent the spring constant. At steady state, when the pointer becomes stable at a particular angle \(\theta\), we can write\[T_d = T_c\]That means\[\frac{1}{2}I^2 \frac{dL}{d\theta} = K\theta\]\[\Rightarrow \theta = \frac{I^2}{2K} \cdot \frac{dL}{d\theta}\]\[\Rightarrow \theta = K’ I^2\]\[\text{Where, K’} = \frac{1}{2K} \cdot \frac{dL}{d\theta}\]We have considered the entire term as constant here for simplicity.
Final Expression of Deflection
\[\theta = K’ I^2 \Rightarrow \theta \propto I^2\]From here, we have observed that the deflection angle is directly proportional to \(I^2\), which is not linear. Therefore, the scale of an attraction type moving iron instrument is nonlinear. The scale is cramped at the beginning and extended at the upper end, as the deflection torque is proportional to \(I^2\), not \(I\).
Therefore, the torque is always directed in the same direction, regardless of the direction of the current. This means the direction of the torque will be the same for positive and negative current. This is one of the advantages of moving iron instruments. Due to this property, we can utilize moving iron instruments in both DC and AC applications.
We can explain it in another simple way. Whatever may be the direction of the current in an electromagnet, the electromagnet always attracts soft iron. This is a very basic observation. This is why, whatever may be the direction of the current, the pointer will always rotate in the same direction. The iron vane, along with the pointer, will rotate about the pivot to come closer to the coil.