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What will be the capacitance of a parallel plate capacitor with air between the plates having capacitance of 8pF (1pF = 10-12 F). How much the capacitance of the capacitor will change if the distance between the plate is reduced to half, and the space between the plates is filled with a substance of dielectric constant 6?
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Capacitance of a Parallel Plate Capacitor with Air

The given capacitance of the parallel plate capacitor with air is 8pF.

Formula for capacitance of a parallel plate capacitor with air is given as:

C = ε₀A/d

Where,


  • C = Capacitance of parallel plate capacitor

  • ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m

  • A = Area of one plate of the capacitor

  • d = Distance between the plates


Substituting the given values in the formula, we get:

C = ε₀A/d = 8.85 x 10^-12 x A/d

C = 8pF = 8 x 10^-12 F

So, 8 x 10^-12 F = 8.85 x 10^-12 x A/d

A/d = 8 x 10^-12 / 8.85 x 10^-12 = 0.9034

Therefore, Area of one plate of the capacitor divided by the distance between the plates is 0.9034.


Capacitance of the Capacitor if Distance Between the Plates is Reduced to Half

When the distance between the plates is reduced to half, the capacitance of the parallel plate capacitor with air is given as:

C' = ε₀A/d'

Where,


  • C' = New capacitance of the parallel plate capacitor

  • ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m

  • A = Area of one plate of the capacitor

  • d' = New distance between the plates = d/2


Substituting the given values in the formula, we get:

C' = ε₀A/d' = 8.85 x 10^-12 x A/(d/2) = 2 x 8.85 x 10^-12 x A/d

C' = 2C = 2 x 8pF = 16pF

Therefore, the new capacitance of the parallel plate capacitor with air when the distance between the plates is reduced to half is 16pF.


Capacitance of the Capacitor if Space Between the Plates is Filled with a Substance of Dielectric Constant 6

When the space between the plates is filled with a substance of dielectric constant 6, the capacitance of the parallel plate capacitor is given as:

C'' = εKA/d

Where,


  • C'' = New capacitance of the parallel plate capacitor

  • ε = Permittivity of the substance between the plates

  • K = Dielectric constant of the substance between the plates = 6

  • A = Area of one plate of the capacitor

  • d = Distance between
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What will be the capacitance of a parallel plate capacitor with air between the plates having capacitance of 8pF (1pF = 10-12 F). How much the capacitance of the capacitor will change if the distance between the plate is reduced to half, and the space between the plates is filled with a substance of dielectric constant 6?
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What will be the capacitance of a parallel plate capacitor with air between the plates having capacitance of 8pF (1pF = 10-12 F). How much the capacitance of the capacitor will change if the distance between the plate is reduced to half, and the space between the plates is filled with a substance of dielectric constant 6? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What will be the capacitance of a parallel plate capacitor with air between the plates having capacitance of 8pF (1pF = 10-12 F). How much the capacitance of the capacitor will change if the distance between the plate is reduced to half, and the space between the plates is filled with a substance of dielectric constant 6? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the capacitance of a parallel plate capacitor with air between the plates having capacitance of 8pF (1pF = 10-12 F). How much the capacitance of the capacitor will change if the distance between the plate is reduced to half, and the space between the plates is filled with a substance of dielectric constant 6?.
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