CBSE Class 12 Physics 2019 Outside Delhi Set 2 Paper

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Question : 9
Total: 9
A 100µF parallel plate capacitor having plate separation of 4‌mm is charged by 200V dc. The source is now disconnected. When the distance between the plates is doubled and at dielectric slab of thickness 4‌mm and dielectric constant 5 is introduced between the plates, how will
(i) its capacitance,
(ii) the electric field between the plates, and
Solution:  
(iii) energy density of the capacitor get affected? Justify your answer in each case.
(i) Change in Capacitance
(ii) Change in Electric field
(iii) Change in Energy density
Dielectric slab of thickness 4‌mm=‌
4
5
‌mm

=0.8‌mm
Effective (air) plate separation
=(4+0.8)‌mm=4.8‌mm
(i) Effective new capacitance
C′=100µF×‌
4‌mm
4.8‌mm
=‌
400
4.8
µ
F

Change on capacitor remains same
Q=C×V=100×10−6×200 =2×10−2C
New p.d. V′=‌
Q
C′
=‌
2×10−2×4.8×10−6
400

=2.4×10−6‌ volt ‌
(ii) Effective new Electric Field,
E′‌=‌
2.4×10−10
4.8×10−3

‌=5×10−8Vm−1
(iii) ‌
‌ New energy stored ‌
‌ Original energy stored ‌
=‌
‌
1
2
C′
V2
1
2
C
V2

‌
C′
C
=‌
400
4.8×100
=0.8

New energy density will be (0.8) of the original density.
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