Do both A and B Section BA variable dielectric capacitive sensor as shown in the following figure isused to measure displacement via a Wheatstone bridge.B1B1.1RsEnCEg = 8.85 x 1012 F/mE=1 for airE=3 for dielectricLength of a capacitor plate = 1 cmWidth of a capacitor plate= 1 cmC2d=5 mmV,=5 Va) Derive the expression for the capacitance Ci and C2 for any displacementх.b) Find the expression/value of x for a balanced bridge, given R= R=100Q.c) Derive the expression for the output voltage in terms of x. Comment onthe sensitivity of this displacement sensor.d)Replace C2 with a fixed capacitance, keeping Ci the same. Find theexpression/value of C2 considering the bridge is balanced at x = 0.Compare and comment on the sensitivity of this device (at x = L/2) withthe sensitivity of the previous sensor (derived in (c)).B1.2 A cantilever-based force sensor setup is shown below:|FFour semiconductor strain gauges are mounted on a cantilever. Thestrain gauges have a gauge factor G, reference resistance Ro andtemperature coefficient ar.a) For the force loading as shown in the figure, write an expression for eachof the resistances for a strain e. Draw the schematic of an appropriateWheatstone bridge incorporating all these four strain gauges.b) Is the output from this Wheatstone bridge affected by temperaturevariations? Derive the proof.

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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.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.27P

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