Problem 1 can move against a spring with constant k [N/m]. By pressing on the movable plate, the distance the plate moves is directly proportional to the force. The plates have an area S and are separated by a distance d. Using Figure P1, and assuming the plate has moved a distance x from the rest position: A force sensor is built as a capacitor with one plate fixed while the other a) Find the relation between measured force and the capacitance of the sensor. b) How can this device be used to measure pressure? Calculate the relation between pressure and capacitance. c) How can this device be used to measure acceleration? Calculate the relation between acceleration and capacitance. Assume that the mass of each plate is m [kg] and the mass of the spring is negligible.

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Problem 1
A force sensor is built as a capacitor with one plate fixed while the other
can move against a spring with constant k [N/m). By pressing on the movable plate, the
distance the plate moves is directly proportional to the force. The plates have an area S and
are separated by a distance d. Using Figure P1, and assuming the plate has moved a distance
x from the rest position:
a) Find the relation between measured force and the capacitance of the sensor.
b) How can this device be used to measure pressure? Calculate the relation between
pressure and capacitance.
c) How can this device be used to measure acceleration? Calculate the relation between
acceleration and capacitance. Assume that the mass of each plate is m [kg] and the
mass of the spring is negligible.
F
Moving plate
Spring
Fixed plate
Figure P1
Transcribed Image Text:Problem 1 A force sensor is built as a capacitor with one plate fixed while the other can move against a spring with constant k [N/m). By pressing on the movable plate, the distance the plate moves is directly proportional to the force. The plates have an area S and are separated by a distance d. Using Figure P1, and assuming the plate has moved a distance x from the rest position: a) Find the relation between measured force and the capacitance of the sensor. b) How can this device be used to measure pressure? Calculate the relation between pressure and capacitance. c) How can this device be used to measure acceleration? Calculate the relation between acceleration and capacitance. Assume that the mass of each plate is m [kg] and the mass of the spring is negligible. F Moving plate Spring Fixed plate Figure P1
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