Question

A quartz crystal has the dimensions of 2mm $\times$ 2mm $\times$ 1 mm. Quartz has the following properties.

$\text{Charge sensitivity}=2pC/N$
$\text{Young's modulus}=9\times {10}^{10}N/m^2$
$\text{Permittivity}=40.6\times {10}^{-12}F/m$

If the crystal is subjected to a dynamic strain of $10\times {10}^{6}m/m,$ then the output voltage generated by the crystal is

• A. 0 V
• B. 443.3 V
• C. 0.443 V
• D. 44.33 V

Answer 1

The correct option is D 44.33 V

For a quartz crystal, output voltage is given by

$V_0=\frac{d}{ϵ}\times t\times P$

$\text{where, d = charge sensitivity; C/N}$

$\text{t = thickness of the crystal}$

$\text{P = Pressure or stress applied on crystal}$

$\because \text{Young's modulus (E)=}\frac{stress\left(P\right)}{strain\left(ϵ\right)}$

$\text{stress (P) = young's modulus}\times \text{strain}$

$=9\times {10}^{10}N/m^2\times 10\times {10}^{-6}=9\times {10}^{5}N/m^2$

$\because V_0=\frac{2\times {10}^{-12}}{40.6\times {10}^{-12}}\times 1\times {10}^{-3}\times 9\times {10}^5=44.33V$