Question

A displacement capacitive transducer consists of two parallel plates of diameter 2cm each separated by an air gap of 0.50 mm and has nominal capacitance of 150 pF. The magnitude of the displacement sensitivity of the transducer is__________pF/mm.

• A. 300

Answer 1

The correct option is A 300
$C=\frac{Aϵ}{d}$

Sensitivity,
$S=\frac{\partial C}{\partial d}$

$=\frac{-Aϵ}{d^2}=\frac{-Aϵ}{d}.\frac{1}{d}$

$=\frac{-C}{d}=\frac{-150}{0.50}=-300pF/mm$

$\text{Magnitude=300pF/mm}$