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A quartz crystal (Young’s modulus, E = 9 * 1010 N / m2) with piezo-electric properties has a diameter of 10 mm and thickness of 2 mm. Its voltage sensitivity constant is 4500 V/ m. If the voltage output is 127.3 V, the applied load is approximately (2002
  • a)
    100 N
  • b)
    200 N
  • c)
    127.3 N
  • d)
    6.4 N
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A quartz crystal (Young’s modulus, E = 9 * 1010 N / m2) with piezo-el...
E = 9 x 1010 N/m2
g = voltage sensitivity = 4500 V/m
V = voltage output = 127.3 V
We know that,
where t = thickness
F = applied load,
A = Area
= 99.98 N ≈ 100 N
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Community Answer
A quartz crystal (Young’s modulus, E = 9 * 1010 N / m2) with piezo-el...
Given information:
- Young’s modulus of the quartz crystal, E = 9 * 10^10 N/m^2
- Diameter of the crystal, d = 10 mm = 0.01 m
- Thickness of the crystal, t = 2 mm = 0.002 m
- Voltage sensitivity constant, K = 4500 V/m
- Voltage output, V = 127.3 V

To find: The applied load

Explanation:
1. Calculate the area of the crystal:
- The area, A = π * (d/2)^2
= π * (0.01/2)^2
= 7.85 * 10^-5 m^2

2. Calculate the change in thickness of the crystal:
- The change in thickness, Δt = V / K
= 127.3 / 4500
= 2.83 * 10^-2 m

3. Calculate the strain in the crystal:
- The strain, ε = Δt / t
= (2.83 * 10^-2) / 0.002
= 1.415

4. Calculate the applied stress on the crystal:
- The stress, σ = E * ε
= 9 * 10^10 * 1.415
= 1.2735 * 10^11 N/m^2

5. Calculate the applied load on the crystal:
- The load, F = A * σ
= 7.85 * 10^-5 * 1.2735 * 10^11
= 1 * 10^7 N

Therefore, the applied load is approximately 100 N. Hence, option A is the correct answer.
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A quartz crystal (Young’s modulus, E = 9 * 1010 N / m2) with piezo-electric properties has a diameter of 10 mm and thickness of 2 mm. Its voltage sensitivity constant is 4500 V/ m. If the voltage output is 127.3 V, the applied load is approximately (2002a)100 Nb)200 Nc)127.3 Nd)6.4 NCorrect answer is option 'A'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A quartz crystal (Young’s modulus, E = 9 * 1010 N / m2) with piezo-electric properties has a diameter of 10 mm and thickness of 2 mm. Its voltage sensitivity constant is 4500 V/ m. If the voltage output is 127.3 V, the applied load is approximately (2002a)100 Nb)200 Nc)127.3 Nd)6.4 NCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quartz crystal (Young’s modulus, E = 9 * 1010 N / m2) with piezo-electric properties has a diameter of 10 mm and thickness of 2 mm. Its voltage sensitivity constant is 4500 V/ m. If the voltage output is 127.3 V, the applied load is approximately (2002a)100 Nb)200 Nc)127.3 Nd)6.4 NCorrect answer is option 'A'. Can you explain this answer?.
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