A coaxial capacitor structure is illustrated in the schematic diagram of Figure Q.2. The capacitor has a length of L. The radius of the inner and outer conductors of the capacitor are a and ß respectively. The gap between the two conductors is filled with a homogeneous charge-free dielectric material with electrical permittivity ɛ. While the outer conductor is grounded, the inner conductor is kept at a constant potential of Vo. Given that L = 5 mm, a = 1 mm, and ß = 3 mm. (a) By means of the Laplace's equation, determine the capacitance's mathematical formulation of the capacitor (b) Determine the suitable dielectric material in Table Q.2 that will produce a capacitance of 5 pF < C < 10 pF (c) Find the maximum voltage Volmax), charge +Qmax and energy We(max) of the capacitor that the dielectric material chosen in Q.2(b) able to withstand. (d) Calculate the resistance of the capacitor L Top View Cross-Sectional View Figure Q.2 Table Q.2 Dielectric Materials Dielectric Constant, ɛr Electrical Resistivity, p. [Nm]| Dielectric Strength, E [kV/m] Tantalum Strontium 1850 1 x 107 8,000 Barium 1250 1x 1012 10,000 Mica 27 1x 1013 100,000 1 x 1015 120,000

A coaxial capacitor structure is illustrated in the schematic diagram of Figure Q.2. The capacitor has a length of L. The radius of the inner and outer conductors of the capacitor are a and ß respectively. The gap between the two conductors is filled with a homogeneous charge-free dielectric material with electrical permittivity ɛ. While the outer conductor is grounded, the inner conductor is kept at a constant potential of Vo. Given that L = 5 mm, a = 1 mm, and ß = 3 mm. (a) By means of the Laplace's equation, determine the capacitance's mathematical formulation of the capacitor (b) Determine the suitable dielectric material in Table Q.2 that will produce a capacitance of 5 pF < C < 10 pF (c) Find the maximum voltage Volmax), charge +Qmax and energy We(max) of the capacitor that the dielectric material chosen in Q.2(b) able to withstand. (d) Calculate the resistance of the capacitor L Top View Cross-Sectional View Figure Q.2 Table Q.2 Dielectric Materials Dielectric Constant, ɛr Electrical Resistivity, p. [Nm]| Dielectric Strength, E [kV/m] Tantalum Strontium 1850 1 x 107 8,000 Barium 1250 1x 1012 10,000 Mica 27 1x 1013 100,000 1 x 1015 120,000

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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