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Question
A dielectric slab of dielectric constant K and thickness t is introduced between the two plates of a capacitor of plate-separation d (>t) and common area A. The capacitance of this system is given as:
`C = (∈_o"A")/((d-t)+(t/k))`
How does the capacitance C modify in each of the following cases?
- The dielectric slab covers half the distance of separation between the two plates.
- The whole space between the plates is filled with the dielectric.
Solution
(a) Using t = `d/2`
Substituting in the given formula and calculating,
C = `(∈_oA)/([(d-d/2)+d/(2K)])`
C = `(2∈_o "AK")/([d(K+1)])`
(b) The whole space between the plates is filled with the dielectric implies, t = d, so C = `(K∈_o"A")/d`
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