CBSE Class 12 Physics 2019 Outside Delhi Set 1 Paper

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Question : 20
Total: 27
A 200µF parallel plate capacitor having plate separation of 5mm is charged by a 100Vdc source. It remains connected to the source. Using an insulated handle, the distance between the plates is doubled and a dielectric slab of thickness 5mm and dielectric constant 10 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 thickness 5mm is equivalent to an air capacitor of thickness =
5
10
mm

Effective separation between the plates with air in between is =(5+0.50)mm=5.5mm
(i) Effective new capacitance
=200µF×
5mm
5.5mm
=
2000
11
µ
F

182µF
(ii) Effective new electric field
=
100V
5.5×103m
=
20000
1.1

18182Vm
(iii)
New energy stored
Original energy stored
=
1
2
C
V2
1
2
C
V2
=
C
C
=
10
11

New Energy density will be (
10
11
)
2
of the original energy density =
100
121
of the original energy density.
[Note: If the student writes C=
Aε0
d

Cm=
KAε0
d

E=
V
d

U=
1
2
ε0
E2
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