Inductive transducers are devices that convert a physical quantity into an electrical signal using the principle of electromagnetic induction. These transducers are widely used for various types of measurements and control applications. One of the main applications of inductive transducers is in displacement and thickness measurement.

Displacement Measurement:
Inductive transducers can be used to measure the displacement of an object. They work by converting the linear or angular displacement into an electrical signal. This is achieved by using a coil and a magnetic core. When the object moves, it changes the position of the magnetic core with respect to the coil, which induces a change in the magnetic field and hence generates an electrical signal proportional to the displacement. This signal can then be further processed and used for various purposes such as position control or feedback.

Thickness Measurement:
Inductive transducers can also be used to measure the thickness of objects. This is done by using a coil and a magnetic core arrangement similar to the displacement measurement. When the object whose thickness is to be measured is placed between the coil and the magnetic core, it changes the position of the magnetic core with respect to the coil, causing a change in the magnetic field and generating an electrical signal proportional to the thickness. This signal can then be calibrated and used to determine the thickness of the object.

Both Displacement and Thickness Measurement:
Since inductive transducers can be used for both displacement and thickness measurements, option C, which states that both displacement and thickness measurement represent the application of inductive transducers, is the correct answer. These measurements find applications in various industries such as manufacturing, automotive, aerospace, and many more.

Conclusion:
Inductive transducers are versatile devices that can be used for measuring various physical quantities. The applications of these transducers include displacement measurement, thickness measurement, and many more. They provide accurate and reliable measurements, making them suitable for a wide range of industrial and scientific applications.