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27. A parallel plate capacitor with capacitance 'C' is charged using a battery of potential difference V. What is the energy stored? How will the energy stored change in each case if
(a) the separation between plates is increased
(b) a dielectric slab is introduced between plates with the battery
(i) disconnected from the capacitor
(ii) still connected to the capacitor.
Justify your answer in each case.

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Solution

Dear Student,
$e n e r g y s t o r e d i s E = \frac{C V^{2}}{2} a . i f t h e s e p e r a t i o n b e t w e e n t h e p l a t e s i n c r e a s e d t h e n t h e c p a c i \tan c e o f t h e c a p a c i t o r w i l l d e c r e a s e s . h e n c e t h e s t o r e d e n e r g y a l s o d e c r e a s e s . b . i . w h e n d i s c o n n e c t e d a n d p l a t e i s i n t r o d u c e d t h e n t h e c a p a c i \tan c e o f t h e c a p a c i t o r w i l l i n c r e a s e . b u t t h e c h a r g e r e m a i n c o n s \tan t Q = C V i f t h e C i n c r e a s e s t h e n i n t h e p r o p o r t i o n a l a m o u n t t h e V s h o u l d d e c r e a s e . \sin c e t h e i r i s V^{2} t e r m s o t h e i r i s f u n d a m n e t a l d e c r e a s e i n s t o r e d e n e r g y . i i . w h e n c o n n e c t e d t o b a t t e r y t h e V r e m a i n c o n s \tan t a n d c a p a c i \tan c e i n c r e a s e s h e n c e t h e s t o r e d e n e r g y w i l l i n c r e a s e a c c o r d i n g t o e q n E = \frac{C V^{2}}{2} R e g a r d s$

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