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A variable dielectric capacitive sensor as shown in the following figure is used to measure displacement via a Wheatstone bridge. Rs E C C2 Eo = 8.85 x 10 12 F/m E=1 for air E=3 for dielectric Length of a capacitor plate = 1 cm Width of a capacitor plate= 1 cm d=5 mm V=5 V Derive the expression for the capacitance Ci and C2 for any displacement х. Find the expression/value of x for a balanced bridge, given R= R=100 a. Derive the expression for the output voltage in terms of x. Comment on the sensitivity of this displacement sensor.

A variable dielectric capacitive sensor as shown in the following figure is used to measure displacement via a Wheatstone bridge. Rs E C C2 Eo = 8.85 x 10 12 F/m E=1 for air E=3 for dielectric Length of a capacitor plate = 1 cm Width of a capacitor plate= 1 cm d=5 mm V=5 V Derive the expression for the capacitance Ci and C2 for any displacement х. Find the expression/value of x for a balanced bridge, given R= R=100 a. Derive the expression for the output voltage in terms of x. Comment on the sensitivity of this displacement sensor.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Section B A variable dielectric capacitive sensor as shown in the following figure is used to measure displacement via a Wheatstone bridge. B1 B1.1 Rs En C Eg = 8.85 x 1012 F/m E=1 for air E=3 for dielectric Length of a capacitor plate = 1 cm Width of a capacitor plate= 1 cm C2 d=5 mm V,=5 V a) Derive the expression for the capacitance Ci and C2 for any displacement х. b) Find the expression/value of x for a balanced bridge, given R= R=100 Q. c) Derive the expression for the output voltage in terms of x. Comment on the sensitivity of this displacement sensor. d) Replace C2 with a fixed capacitance, keeping Ci the same. Find the expression/value of C2 considering the bridge is balanced at x = 0. Compare and comment on the sensitivity of this device (at x = L/2) with the sensitivity of the previous sensor (derived in (c)). B1.2 A cantilever-based force sensor setup is shown below: |F Four semiconductor strain gauges are mounted on a cantilever. The strain gauges have a gauge factor G, reference resistance Ro and temperature coefficient ar. a) For the force loading as shown in the figure, write an expression for each of the resistances for a strain e. Draw the schematic of an appropriate Wheatstone bridge incorporating all these four strain gauges. b) Is the output from this Wheatstone bridge affected by temperature variations? Derive the proof.
Transcribed Image Text:Section B A variable dielectric capacitive sensor as shown in the following figure is used to measure displacement via a Wheatstone bridge. B1 B1.1 Rs En C Eg = 8.85 x 1012 F/m E=1 for air E=3 for dielectric Length of a capacitor plate = 1 cm Width of a capacitor plate= 1 cm C2 d=5 mm V,=5 V a) Derive the expression for the capacitance Ci and C2 for any displacement х. b) Find the expression/value of x for a balanced bridge, given R= R=100 Q. c) Derive the expression for the output voltage in terms of x. Comment on the sensitivity of this displacement sensor. d) Replace C2 with a fixed capacitance, keeping Ci the same. Find the expression/value of C2 considering the bridge is balanced at x = 0. Compare and comment on the sensitivity of this device (at x = L/2) with the sensitivity of the previous sensor (derived in (c)). B1.2 A cantilever-based force sensor setup is shown below: |F Four semiconductor strain gauges are mounted on a cantilever. The strain gauges have a gauge factor G, reference resistance Ro and temperature coefficient ar. a) For the force loading as shown in the figure, write an expression for each of the resistances for a strain e. Draw the schematic of an appropriate Wheatstone bridge incorporating all these four strain gauges. b) Is the output from this Wheatstone bridge affected by temperature variations? Derive the proof.
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