A capacitor consisting of two plates separated by a distance d of 4.25 x 10^-3,

Question

A capacitor consisting of two plates separated by a distance d of 4.25 x 10^-3, with an area A of 8.15 x 10^-4 m^2, is filled with a material whose dielectric constant K is 5.40. The voltage across the capacitor is 12.0 volts

What is the capacitance C?

What is the numerical value of the energy for the capacitor?

What is the value of E for the capacitor in volts per meter?

What is the energy density for the capacitor in joules per meter^3?

What plate area is required if an air filled parallel plate capacitor with a plate separation= 2.6 mm is to havea a capacitance of 22pf?

For the aforementioned parallel plate capacitor with a plate separation=2.6mm, what is the maximum voltage that can be applied without causing dielectric breakdown?

Explanation / Answer

Part 1)

Apply C = kEA/d

C = (5.4)(8.85 X 10^-12)(8.15 X 10^-4)/(4.25 X 10^-3)

C = 9.16 X 10^-12 F (9.16 pF)

Part 2)

E = .5CV^2

E = (.5)(9.16 X 10^-12)(12)^2

E = 6.60 X 10^-10 J

Part 3)

From V = Ed

E = 12/4.25 X 10^-3

E = 2824 V/m

Part 4)

Energy Density = E/volume

Energy Density = 6.60 X 10^-10/(8.15 X 10^-4)(4.25 X 10^-3)

Energy Density = 1.90 X 10^-4 J/m^3

Part 5)

C = kEA/d

22 X 10^-12 = 1(8.85 X 10^-12)(A)/(2.6 X 10^-3)

A = 6.46 X 10^-3 m^3

Part 6)

The dielectric strength of air is 3 X 10^6 V/m, so
V = Ed

V = (3 X 10^6)(2.6 X 10^-3)

V = 7800 V

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