What is the Capacitance of a Capacitor with Two Different Dielectrics?

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SUMMARY

The capacitance of a capacitor with two different dielectrics, where the upper half has a dielectric constant \(\kappa = 4.61\) and the lower half has \(\kappa = 6.9\), can be calculated using the formula \(C_{total} = C_{TOP} + C_{BOTTOM}\). The calculations yield \(C_{TOP} = 1.1756 \times 10^{-9} \, F\) and \(C_{BOTTOM} = 1.7595 \times 10^{-9} \, F\), resulting in a total capacitance of \(C_{total} = 2.9351 \times 10^{-9} \, F\) or 2.9351 nF. The problem neglects edge effects and assumes a plate area of 0.12 m² and a separation of 0.0005 m.

PREREQUISITES
  • Understanding of capacitor fundamentals and capacitance formulas
  • Knowledge of dielectric materials and their properties
  • Familiarity with the constants \(\epsilon_0\) (vacuum permittivity)
  • Basic algebra for manipulating equations
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  • Learn about edge effects in capacitor design
  • Investigate the impact of plate area and separation on capacitance
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DrunkApple
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Homework Statement


A capacitor is constructed from two square
metal plates. A dielectric [itex]\kappa[/itex] = 4.61 fills the
upper half of the capacitor and a dielectric
[itex]\kappa[/itex] = 6.9 fills the lower half of the capacitor.
Neglect edge effects. Calculate the capacitance C of the device.
Answer in units of pF


Homework Equations


C[itex]_{TOP}[/itex] = [itex]\kappa[/itex][itex]\epsilon[/itex]A/d
C[itex]_{bottom}[/itex] = [itex]\kappa[/itex][itex]\epsilon[/itex]A/d
C[itex]_{total}[/itex] = C[itex]_{TOP}[/itex] + C[itex]_{BOTTOM}[/itex]

The Attempt at a Solution


C[itex]_{TOP}[/itex] = [itex]\kappa[/itex][itex]\epsilon[/itex]A/d
= 4.61(8.85419*10[itex]^{-12}[/itex])(.12[itex]^{2}[/itex])/0.0005
= 1.175553098*10[itex]^{-9}[/itex]
C[itex]_{bottom}[/itex] = 6.9(8.85419*10[itex]^{-12}[/itex])(.12[itex]^{2}[/itex])/0.0005
= 1.759504637*10[itex]^{-9}[/itex]
C[itex]_{total}[/itex] = 2.935057735*10[itex]^{-9}[/itex]
Is this correct?
 
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DrunkApple said:

Homework Statement


A capacitor is constructed from two square
metal plates. A dielectric [itex]\kappa[/itex] = 4.61 fills the
upper half of the capacitor and a dielectric
[itex]\kappa[/itex] = 6.9 fills the lower half of the capacitor.
Neglect edge effects. Calculate the capacitance C of the device.
Answer in units of pF
Ummm. Plate size? Plate separation? Are the plates oriented vertically or horizontally?
 

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