# Multiple dielectrics inserted in capacitor

1. Mar 11, 2013

### Woopydalan

1. The problem statement, all variables and given/known data
A parallel-plate capacitor is constructed by filling
the space between two square plates with blocks of three
dielectric materials, as in Figure P26.61. You may assume
that l >> d. (a) Find an expression for the capacitance of
the device in terms of the plate area A and d, κ1, κ2, and
κ3. (b) Calculate the capacitance using the values
A = 1.00 cm2, d = 2.00 mm, κ1 = 4.90, κ2 = 5.60, and
κ3 = 2.10.

2. Relevant equations

3. The attempt at a solution

I understand that κ1 is parallel to κ2 and κ3 and just make a circuit out of it. The problem I'm having is that it is saying the expression for the capacitance of κ1 is

κ1ε(A/2)/d

and for the capacitors of κ2 and κ3

κ2ε(A/2)/(d/2) and κ3(A/2)/(d/2)

However, my question is why for K2 and K3 isn't it Kε(A/4)/(d/2) since they only consist of one fourth the area of the whole capacitor

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2. Mar 11, 2013

### Staff: Mentor

K1 has half of the area of each square plate. The combination K2 with K3 can be viewed as a pair of capacitors in series.