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?

Question

Infinity Learn · Accepted Answer

Energy stored in capacitor (i)  $$V1=12C1V2=12$$ε$$0AdV2=12$$ε$$0lwdV2$$ Similarly inii,​parts with air and dielectric can be considered in parallel​$$U2=12C2V2=12$$ε$$0A1d+$$ε$$0A2dV2=12$$ε$$0l$$−$$xwd+4$$ε$$0xwdV2$$ & also given ​$$U2=2U1$$​⇒l−$$x+4x=2l$$​⇒$$x=l/3$$

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