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Q.

A parallel plate capacitor has plate of length ‘ l’ , width ‘w’ and separation of plates is ‘d’. It is connected to a battery of emf V. A dielectric slab of the same thickness ‘d’ and of dielectric constant k = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?

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a

l/4

b

l/2

c

2l/3

d

l/3

answer is D.

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Detailed Solution

Energy stored in capacitor (i)  V1=12C1V2=12ε0AdV2=12ε0lwdV2 Similarly inii,​parts with air and dielectric can be considered in parallel​U2=12C2V2=12ε0A1d+ε0A2dV2=12ε0l−xwd+4ε0xwdV2 & also given ​U2=2U1​⇒l−x+4x=2l​⇒x=l/3
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