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Question

# Consider a parallel plate capacitator of capacity 10 μF filled with air. When the gap between the plates is filled partly with a dielectric of dielectric constant 4, as shown in figure, the new capacity of the capacitator is (A is the area of plates):

A
20μF
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B
40μF
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C
2.5μF
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D
25μF
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Solution

## The correct option is D 25μFSuch a configuration can be thought of as a parallel combination of two capacitors- one with area A/2 and dielectric and another with same area and without dielectric.C1=ϵ0A2d; (for air in between)In second case k=4C2=4ϵ0A2d=2ϵ0AdHence, effective capacitance is C=C1+C2=2.5ϵ0Ad=2.5C0=25 μF

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