Question

A quartz crystal (Young's modulus, $(E=9\times {10}^{10}N/m^2)$ with piezoelectric properties has a diameter of 10 mm and thickness of 2 mm. Its voltage sensitivity constant is $4500V/\mu m.$ If the voltage output is 127.3 V, then the applied load is approximately

• A. 100N
• B. 200N
• C. 127.3 N
• D. 6.4 N

Answer 1

The correct option is A 100N

$E=9\times {10}^{10}N/m^2$

$V=gtp=gE\left(\Delta t\right)$

$\Delta T=\frac{V}{gE}=\frac{127.3V}{4500V/\mu m}$

$=0.02828\mu m$

$F=EA\left(\frac{\Delta t}{t}\right)$

$=9\times {10}^{10}\times \frac{0.02828\times {10}^{-6}}{2\times {10}^{-3}}\times \frac{\pi (10\times {10}^{-3}{)}^2}{4}$

$F=99.49N\approx 100N$