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A parallel-plate capacitor, with air in between the plates, has capaci

June 1, 2025 by rawan239

A parallel-plate capacitor, with air in between the plates, has capacitance C. Now the space between the two plates of the capacitor is filled with a dielectric of dielectric constant 7. Then the value of the capacitance will become

C

C/7

7C

14C

This question was previously asked in

UPSC CDS-1 – 2017

Download PDF Attempt Online

The correct answer is C) 7C.

The capacitance of a parallel-plate capacitor is given by C = ε * A / d, where ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between them. When there is air (or vacuum) between the plates, the permittivity is approximately ε₀, and the capacitance is C = ε₀ * A / d. When the space is filled with a dielectric material of dielectric constant κ, the permittivity changes to ε = κ * ε₀. Therefore, the new capacitance C’ becomes C’ = (κ * ε₀) * A / d = κ * (ε₀ * A / d). Given that the dielectric constant κ = 7, the new capacitance is C’ = 7 * C.

Introducing a dielectric material between the plates of a capacitor increases the electric field strength between the plates for the same voltage, or reduces the voltage across the plates for the same charge. This results in the capacitor being able to store more charge at the same voltage, effectively increasing its capacitance.

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