Question

A quartz piezo-electric crystal having dimensions of $5mm\times 5mm\times 1mm$ and a voltage sensitivity of $0.05V-m/N$ is used for force measurement. The voltage generated due to applied force is given to an amplifier of amplification factor $500$. If the voltage developed at amplifier output is $100V$. Then the amount of applied force is ____ $N$.

• A. 0.1

Answer 1

The correct option is A 0.1
$V_0=[g\times t\times \frac{F}{A}]\times \text{gain}$

$\text{where,}g=\text{voltage sensitivty}(V-m/N)$

$t=\text{thickness of crystal}\left(m\right)$

$F=\text{applied force}\left(N\right)$

$A=\text{area of cross sectional}\left(m^2\right)$

$F=\frac{V_0\times A}{g\times t\times \text{gain}}$

$=\frac{100\times 5\times 5\times {10}^{-6}}{0.05\times 1\times {10}^{-3}\times 500}$

$=0.1N$