Consider a parallel-plate capacitor that is partially filled with a dielectric of dielectric constant k. the dielectric has the same same height as the separation of the plates of the capacitor but fills a fraction f of the area of the capacitor. the capacitance of the capacitor when the dielectric is completely removed is c0.

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Luna Phillips

Physics

15 April, 05:45

Consider a parallel-plate capacitor that is partially filled with a dielectric of dielectric constant k. the dielectric has the same same height as the separation of the plates of the capacitor but fills a fraction f of the area of the capacitor. the capacitance of the capacitor when the dielectric is completely removed is c0.

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Hayden Huber · Answer 1

The formula for the capacitance of the capacitor made of two parallel plates with a dielectric in between them is

C = k A f / d

When the dielectric is removed, air is between the plates with a permissivity of 1

Co = A / d

The height of the dielectric is the same as the separation of the plates. So,

k h lf / C = h l / Co

The ratio of the lengths of the dielectric and the plates is

lf / l = C / k Co