Question

A dielectric of dielectric constant 3 fills three fourth of the space between the plates of a parallel plate capacitor. What percentage of the energy is stored in the dielectric?

Answer 1

Let d be the distance b/w the plates.
thickness t = 3/4.
If C is the capacitance , ε₀ is the permittivity , q is the charge and v is the Potential difference then
we know the relative equation .

Energy stored in a capacitor first .

$U_{1} = \frac{1}{2} \frac{Q^2}{C_{1}}$    as Q is the constant.
if,  C = ε₀A / d   then 
U₁ = Q².d / 2ε₀.A ----→(i)

Energy stored in second capacitor.

$U_{2} = \frac{1}{2} \frac{Q^2}{C_{2}}$ 
as 3/4 is the the thickness ,similarly again,
U₂ = Q².d / 4ε₀.A-----→(ii)

dividing (ii) with (i)
___________
U₂ / U₁ = 1/2
___________

Or the energy stored in the dielectric is 50% .


Hope it Helps.