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Question

A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be
1200430_8e7d830c81fd4523b6b212dfc249ed45.png
  1. 400%
  2. 66.6%
  3. 33.3%
  4. 200%

A
200%
B
66.6%
C
33.3%
D
400%
Solution
Verified by Toppr

Initial capacitance=ϵAd
When it is half filled by a dielectric of dielectric constant k then
C1=kϵAd2=2kϵAd
and C2=ϵAd2=2ϵAd
1C=1C1+1C2
=d2ϵA(1k+1)
=d2ϵA(15+1)
=d2ϵA(65)
=3d5ϵA
C=5ϵA3d
Hence, % increase in capacitance is
=⎜ ⎜ ⎜5ϵAdϵAdϵAd⎟ ⎟ ⎟×100=23×100=66.6%

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