A parallel plate capacitor is constructed such that there are two different dielectric materials in between the plates, each occupying half the space in between . Still this capacitor can be modeled as a simple parallel plate capacitor with same total area A, plate separation d, but with an equivalent dielectric constant Keq. What is Keq? (Your final answer will be in terms of the two K's, and for a start, you should think in terms of potential being same all over the surface for any given plate)
_________
l I I
l K1 I K2 l d
l____I____l
with an area A
I know the capacitance of a parallel-plate capacitor filled with a dielectric is C = KEoA / d
But I am not quite sure what to do if K is split into K1 and K2 as displayed in the picture above. Do I set them equal to each other?
Any help would be appreciated!
Answers & Comments
Verified answer
look at it as two capacitors in series, with a common plate between the two.
C1 = k₁ε₀A/d
C2 = k₂ε₀A/d
Two caps in series, 1/C = 1/C1 + 1/C2
1/C = d/k₁ε₀A + d/k₂ε₀A/d
1/C = (d/ε₀A) * (1/k₁ + 1/k₂)
assume an equivalent k for the combination
1/C = d/kε₀A = (d/ε₀A) * (1/k₁ + 1/k₂)
1/k = 1/k₁ + 1/k₂
or k = k₁k₂/(k₁ + k₂)
.
In a circuit containing a parallel-plate capacitor and a means source (at the same time with a battery), the means source promises power for expenditures to bypass to the plates of the capacitor - damaging expenditures on one plate and useful ones on the different plate. This effectively creates an electric powered field between the plates of the capacitor. This field shops power and this is the flexibility that flows in the course of the area between the plates - no longer the costs. The bypass of power between the plates effectively keeps the continuity of 'modern-day' between the capacior plates.