Question

The voltage output of piezoelectric crystal is measured as 15V for certain amount of force. The charge sensitivity of the crystal is 120 PC/N and the permittivity of the crystal is 8nF/m. If the crystal is having 5 mm diameters and 0.1mm thickness then the amount of force applied on the crystal (in N) is?

• A. 196.35

Answer 1

The correct option is A 196.35
$\text{The voltage output}{V}_0=\text{g.t.p}$

$\text{g}=\text{Voltage sensitivity}=\frac{\text{Charge sensitivity}}{\text{Permittivity}}$

$\therefore \text{g}=\frac{d}{ϵ}$

$P=Pressure=\frac{\text{Force}}{\text{Area}}=\frac{F}{A}$

$Area=\frac{\pi }{4}{D}^2\Rightarrow \text{D = Diameter}$

$\text{Combining all and putting the value}$

$V_o=\frac{d}{ϵ}\times t\times \frac{F}{A}$

$\Rightarrow F=\frac{V_o\times ϵ\times A}{d\times t}$

$=\frac{15\times 8\times {10}^{-9}\times \frac{\pi }{4}(5\times {10}^{-3}{)}^2}{120\times {10}^{-12}\times 0.1\times {10}^{-3}}$

$=196.349$

$F\approx 196.35N$