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A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine
(a) the force to which it is subjected,
(b) the capacitance of the transducer,
(c) the charge generated,
(d) the voltage developed
Correct answer is '0.5'. Can you explain this answer?
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Verified Answer
A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, ...
Given,Input displacement = 10-9 m
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y = 8.6 x 1010 N/m2
Dielectric constant = 4 x 10-11 F/m
Charge sensitivity, d = 2 x 10-12 C/N
Charge generated, Q = d x F
where, d = charge sensitivity
f = force in N
A = πr2
Strain in transducer
= 1.08 x 106 N
Q = d x F
= 1.08 x 106 x 2 x 10-12
= 2.16 x 10-6 C
Voltage generated, E0 = gtp
Most Upvoted Answer
A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, ...
Given data:
Diameter of the transducer (d) = 8 mm = 8 x 10^-3 m
Thickness of the transducer (h) = 4 mm = 4 x 10^-3 m
Charge sensitivity (K) = 2 x 10^-12 C/N
Dielectric constant (ε) = 4 x 10^-11 F/m
Modulus of elasticity (E) = 8.6 x 10^10 N/m^2
Input displacement (x) = 10^9 m
(a) Force to which the transducer is subjected:
The force applied to the transducer can be calculated using the equation:
Force (F) = K * x
Substituting the given values:
F = (2 x 10^-12 C/N) * (10^9 m)
F = 2 N
(b) Capacitance of the transducer:
The capacitance of the transducer can be calculated using the equation:
Capacitance (C) = ε * (A / h)
where A is the area of the transducer.
The area of the transducer can be calculated using the equation:
A = π * (d/2)^2
Substituting the given values:
A = π * (8 x 10^-3 m / 2)^2
A = π * (4 x 10^-3 m)^2
A = π * 16 x 10^-6 m^2
A = 50.24 x 10^-6 m^2
Now, substituting the values of ε and A in the capacitance equation:
C = (4 x 10^-11 F/m) * (50.24 x 10^-6 m^2 / 4 x 10^-3 m)
C = 4 x 10^-11 F/m * 12.56 x 10^-3 m
C = 50.24 x 10^-14 F
C = 5.024 x 10^-12 F
(c) Charge generated:
The charge generated can be calculated using the equation:
Charge (Q) = C * V
where V is the voltage developed.
(d) Voltage developed:
The voltage developed can be calculated using the equation:
Voltage (V) = E * x
Substituting the given values:
V = (8.6 x 10^10 N/m^2) * (10^9 m)
V = 8.6 x 10^19 V
Now, substituting the values of C and V in the charge equation:
Q = (5.024 x 10^-12 F) * (8.6 x 10^19 V)
Q = 43.2064 x 10^7 C
Q = 4.32064 x 10^8 C
To summarize:
(a) The force to which the transducer is subjected is 2 N.
(b) The capacitance of the transducer is 5.024 x 10^-12 F.
(c) The charge generated is 4.32064 x 10^8 C.
(d) The voltage developed is 8.6 x 10^19 V.
Diameter of the transducer (d) = 8 mm = 8 x 10^-3 m
Thickness of the transducer (h) = 4 mm = 4 x 10^-3 m
Charge sensitivity (K) = 2 x 10^-12 C/N
Dielectric constant (ε) = 4 x 10^-11 F/m
Modulus of elasticity (E) = 8.6 x 10^10 N/m^2
Input displacement (x) = 10^9 m
(a) Force to which the transducer is subjected:
The force applied to the transducer can be calculated using the equation:
Force (F) = K * x
Substituting the given values:
F = (2 x 10^-12 C/N) * (10^9 m)
F = 2 N
(b) Capacitance of the transducer:
The capacitance of the transducer can be calculated using the equation:
Capacitance (C) = ε * (A / h)
where A is the area of the transducer.
The area of the transducer can be calculated using the equation:
A = π * (d/2)^2
Substituting the given values:
A = π * (8 x 10^-3 m / 2)^2
A = π * (4 x 10^-3 m)^2
A = π * 16 x 10^-6 m^2
A = 50.24 x 10^-6 m^2
Now, substituting the values of ε and A in the capacitance equation:
C = (4 x 10^-11 F/m) * (50.24 x 10^-6 m^2 / 4 x 10^-3 m)
C = 4 x 10^-11 F/m * 12.56 x 10^-3 m
C = 50.24 x 10^-14 F
C = 5.024 x 10^-12 F
(c) Charge generated:
The charge generated can be calculated using the equation:
Charge (Q) = C * V
where V is the voltage developed.
(d) Voltage developed:
The voltage developed can be calculated using the equation:
Voltage (V) = E * x
Substituting the given values:
V = (8.6 x 10^10 N/m^2) * (10^9 m)
V = 8.6 x 10^19 V
Now, substituting the values of C and V in the charge equation:
Q = (5.024 x 10^-12 F) * (8.6 x 10^19 V)
Q = 43.2064 x 10^7 C
Q = 4.32064 x 10^8 C
To summarize:
(a) The force to which the transducer is subjected is 2 N.
(b) The capacitance of the transducer is 5.024 x 10^-12 F.
(c) The charge generated is 4.32064 x 10^8 C.
(d) The voltage developed is 8.6 x 10^19 V.
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A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine(a) the force to which it is subjected,(b) the capacitance of the transducer,(c) the charge generated,(d) the voltage developedCorrect answer is '0.5'. Can you explain this answer?
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A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine(a) the force to which it is subjected,(b) the capacitance of the transducer,(c) the charge generated,(d) the voltage developedCorrect answer is '0.5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine(a) the force to which it is subjected,(b) the capacitance of the transducer,(c) the charge generated,(d) the voltage developedCorrect answer is '0.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine(a) the force to which it is subjected,(b) the capacitance of the transducer,(c) the charge generated,(d) the voltage developedCorrect answer is '0.5'. Can you explain this answer?.
A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine(a) the force to which it is subjected,(b) the capacitance of the transducer,(c) the charge generated,(d) the voltage developedCorrect answer is '0.5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine(a) the force to which it is subjected,(b) the capacitance of the transducer,(c) the charge generated,(d) the voltage developedCorrect answer is '0.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine(a) the force to which it is subjected,(b) the capacitance of the transducer,(c) the charge generated,(d) the voltage developedCorrect answer is '0.5'. Can you explain this answer?.
Solutions for A piezoelectric transducer having diameter = 8 mm, thickness = 4 mm, charge sensitivity = 2 x 10-12 C/N, dielectric constant = 4 x 10-11 F/m and modulus of elasticity = 8.6 x 1010 N/m2 is used for the measurement of small displacement. For an input displacement of 109 m, determine(a) the force to which it is subjected,(b) the capacitance of the transducer,(c) the charge generated,(d) the voltage developedCorrect answer is '0.5'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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