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Ampere-Maxwell's Law: Problem-Solving01:17

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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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In electrical power systems, understanding the capacitance of transmission lines is fundamental for efficient operation.
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A displacement current is analogous to a real current in Ampère's law, participating in Ampère's law the same way as the usual conduction current. However, it is produced by a changing electric field. Displacement current is defined in terms of a time-varying electric field, and also has an associated displacement current density. By adding a term accounting for displacement current, Maxwell modified the existing Ampère's law, which is now called generalized Ampère's law.
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A modified linear capacitive displacement transducer for any range.

Saikat Kumar Bera1, Moumita Chakraborty2,3, Pradip Kumar Sadhu3

  • 1Dept. of Electronics & Communication Engineering, Chaibasa Engineering College, Jharkhand, 833201, India.

Heliyon
|November 5, 2024
PubMed
Summary

A novel linear capacitive displacement transducer minimizes errors for accurate measurements. This innovative design ensures a linear output across all ranges, enhancing precision in displacement sensing applications.

Keywords:
Combined cylindrical-perpendicular plate capacitorDisplacement transducerInsulating cylinderMovable conducting diskNon-inductive short windingOp-amp

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Area of Science:

  • Electrical Engineering
  • Instrumentation and Measurement

Background:

  • Capacitive displacement transducers are widely used for non-contact measurement.
  • Traditional designs often suffer from non-linearity and various error sources.
  • Minimizing these errors is crucial for high-precision applications.

Purpose of the Study:

  • To develop a modified linear capacitive displacement transducer.
  • To minimize measurement and non-linearity errors.
  • To achieve a linear output related to displacement for any range.

Main Methods:

  • A modified transducer design featuring sensing and reference capacitors.
  • Each capacitor utilizes a noninductive double layer short-circuited winding on a hollow cylinder.
  • A displaceable conducting disk within the sensing cylinder and a fixed disk in the reference cylinder.
  • Measurement of the difference in combined cylindrical-perpendicular plate capacitances.

Main Results:

  • The developed transducer exhibits a linear relationship between output and displacement over the entire sensing range.
  • Errors due to atmospheric parameters, parasitic fringe capacitance, stray capacitance, and plate shifting are significantly minimized.
  • The cancellation of non-linearity factors in the differential measurement ensures high accuracy.
  • Experimental results validate the derived characteristic equations with excellent accuracy and repeatability.

Conclusions:

  • The modified linear capacitive displacement transducer effectively overcomes limitations of conventional designs.
  • The transducer provides highly accurate and linear displacement measurements.
  • This technology offers a robust solution for precise displacement sensing in various industrial and scientific fields.