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Question : 20
Total: 27
A 200 µ F parallel plate capacitor having plate separation of 5 mm is charged by a 100 V dc source. It remains connected to the source. Using an insulated handle, the distance between the plates is doubled and a dielectric slab of thickness 5 mm and dielectric constant 1 0 is introduced between the plates. Explain with reason, how the (i) capacitance, (ii) electric field between the plates, (iii) energy density of the capacitor will change?
Solution:
(i) Change in capacitance
(ii) Change in electric field
(iii) Change in electric density
Dielectric slab of thickness5 mm is equivalent to an air capacitor of thickness =
mm
Effective separation between the plates with air in between is= ( 5 + 0.50 ) mm = 5.5 mm
(i) Effective new capacitance
= 200 µ F ×
=
µ F
≈ 182 µ F
(ii) Effective new electric field
=
=
≈ 18182 V ∕ m
(iii)
=
=
=
New Energy density will be(
) 2 of the original energy density =
of the original energy density.
[Note: If the student writesC =
C m =
E ′ =
U =
ε 0 E 2
(ii) Change in electric field
(iii) Change in electric density
Dielectric slab of thickness
Effective separation between the plates with air in between is
(i) Effective new capacitance
(ii) Effective new electric field
(iii)
New Energy density will be
[Note: If the student writes
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