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

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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]
Strontium
Barium
Tantalum
Mica
1850
1250
27
1 x 107
8,000
1 × 1012
10,000
1x 1013
100,000
1 x 1015
120,000
Transcribed Image Text: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] Strontium Barium Tantalum Mica 1850 1250 27 1 x 107 8,000 1 × 1012 10,000 1x 1013 100,000 1 x 1015 120,000
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