Question

Capacitive transducer displays

• A. \( \text{Linear behaviour} \)
• B. \( \text{Non-linear behaviour} \)
• C. \( \text{Like y = 2x curve} \)
• D. \( \text{Like y = mx+b curve} \)

Hint:

Remember that the capacitance formula $C = \frac{\epsilon A}{d}$ is key to understanding the behavior of capacitive transducers. If the variable being measured directly affects the distance ($d$), the relationship is inverse, leading to non-linearity. If the variable affects the area ($A$) or permittivity ($\epsilon$), the relationship can be linear. Always consider which parameter of the capacitor is changing to determine linearity.

Answer 1

The Correct Option is B

A capacitive transducer works on the principle of change in capacitance due to a change in the physical quantity being measured. The capacitance ($C$) of a parallel plate capacitor is given by the formula: $$ C = \frac{\epsilon A}{d} $$ where:

• $C$ is the capacitance
• $\epsilon$ is the permittivity of the dielectric material between the plates
• $A$ is the area of overlap of the plates
• $d$ is the distance between the plates

When a capacitive transducer measures displacement by varying the distance ($d$) between the plates, the relationship between capacitance and displacement is inverse: $C \propto \frac{1}{d}$. This inverse relationship means that the output (capacitance) is not directly proportional to the input (displacement). Therefore, the behavior is inherently non-linear.

• (A) Linear behaviour: This would imply a direct proportionality, which is not the case for capacitance varying with distance.
• (B) Non-linear behaviour: As explained by the inverse relationship, this is the correct description.
• (C) Like y = 2x curve: This represents a linear relationship, which is incorrect.
• (D) Like y = mx+b curve: This also represents a linear relationship, which is incorrect.

While some linearization techniques can be applied in practice (e.g., using a differential capacitive transducer), the fundamental behavior of a single capacitive transducer with varying distance is non-linear.