Question

A capacitive transducer is used for measurement of displacement using an opertional amplifier as shown in the figure.


If the capacitance of capacitive transducer is given by $C_x={ϵ}_{0}A/x$. where $A$ is the area of the plates and $x$ is distance between the plate. Then the relationship between the output voltage $V_0$ and input displacement is given by

• A. $V_0\propto \frac{1}{x}$
• B. $V_0\propto x^2$
• C. $V_0\propto x$
• D. $V_0\propto \sqrt{x}$

Answer 1

The correct option is C $V_0\propto x$

$\text{The circuit is working in inverting mode}$

$\therefore \frac{V_0}{V_i}=\frac{-Z_1}{Z_x}=\frac{-1}{j\omega C_x}\times j\omega C_1=-\frac{C_1}{{ϵ}_{0}A/x}$

$V_0=\left[\frac{-C_1{V}_i}{{ϵ}_{0}A}\right]x=Kx$

$V_0\propto x$