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A reactive bridge shown in Figure 1 is used for a position measurement, where Cx acts as a capacitive position sensor. The dimension and position of Cx are given in Figure 2. When external force F is applied to the top plane, displacement, AL, occurs along the horizontal direction (Figure 2). It is known that when the bridge is balanced, C₁ is 16.6 nF. Note: the relative permittivity of the dielectric is 80 and the permittivity of free space (vacuum) is 8.85x10-12 Fm¹. R₁=10 k R₂=4.7 k Vin (9-12 V, 1 kHz) AL L=0.3m Dielectric L F d=0.001 m Width: w=0.2 m Figure 1. Reactive bridge Figure 2. Size and position of Cx (a) Determine the displacement, AL (assume that the field of fringing can be ignored) (Tip: when the bridge is balanced, the ratio of R, and R₂ must be equal to ratio of Cx and C₁, i.e., R₁/R₂=C/C₁, as the reactance of capacitor: X= 1/2fC and current through capacitor: /=V/Xc) (b) Discuss if the amplitude and frequency of Vin affect the results.

A reactive bridge shown in Figure 1 is used for a position measurement, where Cx acts as a capacitive position sensor. The dimension and position of Cx are given in Figure 2. When external force F is applied to the top plane, displacement, AL, occurs along the horizontal direction (Figure 2). It is known that when the bridge is balanced, C₁ is 16.6 nF. Note: the relative permittivity of the dielectric is 80 and the permittivity of free space (vacuum) is 8.85x10-12 Fm¹. R₁=10 k R₂=4.7 k Vin (9-12 V, 1 kHz) AL L=0.3m Dielectric L F d=0.001 m Width: w=0.2 m Figure 1. Reactive bridge Figure 2. Size and position of Cx (a) Determine the displacement, AL (assume that the field of fringing can be ignored) (Tip: when the bridge is balanced, the ratio of R, and R₂ must be equal to ratio of Cx and C₁, i.e., R₁/R₂=C/C₁, as the reactance of capacitor: X= 1/2fC and current through capacitor: /=V/Xc) (b) Discuss if the amplitude and frequency of Vin affect the results.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2. A reactive bridge shown in Figure 1 is used for a position measurement, where Cx acts as a capacitive position sensor. The dimension and position of Cx are given in Figure 2. When external force F is applied to the top plane, displacement, AL, occurs along the horizontal direction (Figure 2). It is known that when the bridge is balanced, C₁ is 16.6 nF. Note: the relative permittivity of the dielectric is 80 and the permittivity of free space (vacuum) is 8.85x10-12 Fm¨¹. R₁=10 k R₂=4.7 k ....….…... Vin (9-12 V, 1 kHz) C₁ Cr ΔΕ L=0.3m Dielectric L F d=0.001 m Width: w=0.2 m Figure 1. Reactive bridge Figure 2. Size and position of Cx (a) Determine the displacement, AL (assume that the field of fringing can be ignored) (Tip: when the bridge is balanced, the ratio of R, and R₂ must be equal to ratio of Cx and C₁, i.e., R₁/R₂=C/C₁, as the reactance of capacitor: X= 1/2fС and current through capacitor: /=V/Xc) (b) Discuss if the amplitude and frequency of Vin affect the results.
Transcribed Image Text:2. A reactive bridge shown in Figure 1 is used for a position measurement, where Cx acts as a capacitive position sensor. The dimension and position of Cx are given in Figure 2. When external force F is applied to the top plane, displacement, AL, occurs along the horizontal direction (Figure 2). It is known that when the bridge is balanced, C₁ is 16.6 nF. Note: the relative permittivity of the dielectric is 80 and the permittivity of free space (vacuum) is 8.85x10-12 Fm¨¹. R₁=10 k R₂=4.7 k ....….…... Vin (9-12 V, 1 kHz) C₁ Cr ΔΕ L=0.3m Dielectric L F d=0.001 m Width: w=0.2 m Figure 1. Reactive bridge Figure 2. Size and position of Cx (a) Determine the displacement, AL (assume that the field of fringing can be ignored) (Tip: when the bridge is balanced, the ratio of R, and R₂ must be equal to ratio of Cx and C₁, i.e., R₁/R₂=C/C₁, as the reactance of capacitor: X= 1/2fС and current through capacitor: /=V/Xc) (b) Discuss if the amplitude and frequency of Vin affect the results.
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