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Question

I have multiple dielectrics (of surface area in contact with capacitor as A1,A2andA3) in my capacitor inserted as shown. What is my new capacitance?

A
ε0d(k1+k2+k3)A
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B
ε0dA(k1+k2+k3)
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C
ε0d(k1A1+k2A2+k3A3)
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D
ε0d(A1+A2+A3)k1
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Solution

The correct option is C ε0d(k1A1+k2A2+k3A3)
As all the dielectric share the same conductor on either side, we can consider the situation to be three capacitor in parallel with each other. Something like this

The capacitance of any of these capacitor would be C=kε0Ad So, Cnet=C1+C2+C3 (Because all of them are in parallel)
Cnet=ε0d(k1A1+k2A2+k3A3)

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