A Quartz piezo-electric crystal having a thickness of 2 mm and voltage sensitivity of 0.055 V-m/N is subjected to a pressure of 1.5 MN/2. Calculate the voltage output. If the permittivity of quartz is 40.6 X 10−12 F/m, calculate its charge sensitivity.

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Answer 1

The charge sensitivity is approximately 3.3495 × 10⁻¹² C.

How to calculate the value

First, let's convert the pressure from mega-newtons to newtons:

1 MN = 1,000,000 N.

P = 1.5 MN/2 = (1.5 * 1,000,000 N) / 2 = 750,000 N.

Now we can calculate the voltage output:

V = (0.002 m) * (0.055 V-m/N) * (750,000 N).

V = 0.0825 V.

Therefore, the voltage output is 0.0825 V.

To calculate the charge sensitivity, we can use the equation:

Q = C * V,

where:

Q is the charge sensitivity,

C is the permittivity of quartz (40.6 × 10^−12 F/m), and

V is the voltage output (0.0825 V).

Let's substitute the values into the equation:

Q = (40.6 × 10⁻¹² F/m) * (0.0825 V).

Q = 3.3495 × 10⁻¹² C.

Therefore, the charge sensitivity is approximately 3.3495 × 10⁻¹² C.

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