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Question

Derive an expression for the capacitance of a parallel plate capacitor. Why does the capacitance increase by using dielectric in capacitor?

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Solution

Consider parallel plate capacitor is place in vacuum and permittivity of vacuum is given by ϵo. Then,
Electric fields between the plates of capacitor is given by,
E=σϵo=QAϵo
potential difference between the plates is given by,
V=Ed=QdAϵo...(1)
But,
Capacitance = C=QV=ϵoAd ... (from eq(1))

If we place dielectric medium in between the plates of capacitor then permittivity of medium increases and
it is denoted by ϵm.Then new capacitance will be,

Capacitance = C=QV=ϵmAd ...(2)...(ϵm>ϵo)

From equation (2) it is clear that capacitance increases when the dielectric is inserted between the plates of capacitor.

780329_772238_ans_109e328c01114e60a6a0857141205c89.gif

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