An inductive transducer works on the basic principle of change in inductance due to any change in the measurand. A change in measurand changes the flux and this change in flux changes the inductance. This change in inductance can be calibrated in terms of measurand.

Inductive transducers works on one of the following principles

**Change of self inductance****Change of mutual inductance****Production of eddy current**

**Change of self inductance**

The self inductance of a coil is given by

Where** N** is the number of turns and

**is the reluctance of the magnetic circuit.**

*R*Also, the reluctance R is given by,

Then,

Where ** μ** is the effective permeability of the medium,

**is the length of the coil and**

*l***is the cross-sectional area of the coil.**

*A*Let **G=A/l**, known as geometric form factor. Therefore

That is, the self-inductance can be changed by a variation in *N*,** G** or

**. If some physical quantity is able to change any of these parameters, then that quantity can be directly measured in terms of inductance.**

*μ*## Change of mutual inductance

Mutually coupled multiple coils are used in this principle. The mutual inductance can be then changed by varying the self-inductance of the coils.

Let’s take two coils and suppose their self-inductance are L_{1} and L_{2}. Then mutual inductance between these two coils is given by,

Where ** K** is the coefficient of coupling.

It is clear that the mutual inductance can be changed if the self-inductance of the coils or the coefficient of coupling is varied. The coefficient of coupling depends on distance, separation and orientation between these two coils.

To measure displacement, one coil is fixed and the other coil is connected to the moving object. The coefficient of coupling changes with varying distance and hence the mutual inductance also changes. This change in mutual inductance can be calibrated in terms of displacement.

## Production of Eddy current

When a coil is placed near to a coil carrying alternating current (AC), a circulating current called **Eddy current** is induced in the coil. This circulating current produces its own flux and tries to reduce the flux of the coil carrying the current which in turn changes the inductance of the coil.

When the coils are nearer, the eddy current produced is higher and the reduction in inductance also increases. So inductance can be varied by a variation of distance between two coils.