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Question

A parallel plate capacitor of capacitance C is equally filled with parallel layers of materials of dielectric constants K1 and K2. Then the ratio of new capacitance to the previous capacitance is

A
2K1K2K1+K2
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B
K1+K2
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C
K1K2K1+K2
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D
None of the above
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Solution

The correct option is A 2K1K2K1+K2
We can redraw circuit as

C1=K1ε0Ad/2=2K1ε0Ad
C2=K2ε0Ad/2=2K2ε0Ad
Now,
Ceq=C1×C2C1+C2
Ceq=2K1ε0Ad×2K2ε0Ad2K1ε0Ad+2K2ε0Ad

On Solving we get
Ceq=2K1K2[ε0Ad][K1+K2]
Now,
CfinalCinitial=2K1K2(K1+K2).[ε0Ad]ε0Ad=2K1K2(K1+K2)

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