Question

# A parallel plate capacitor with air as the medium between the plates has a capacitance of 10μ F. The area of the capacitor is divided into two equal halves and filled with two media having dielectric constant k1=2 and k2=4. The capacitance will now be :

A
10μ F
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B
20μ F
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C
30μ F
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D
40μ F
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Solution

## The correct option is C 30μ FInitial capacitance is given as C=10μF⇒C=ε0Ad=10μFNew arrangement acts as two capacitors C1 and C2 connected in parallel.Thus capacitance of each part C1=k1ε0A1d and C2=k2ε0A2dEquivalent capacitance of parallel combination Cp=C1+C2=(k1+k2)ϵ0(A1+A2)d ⟹ Cp=(k1+k2)ϵ0A2d (∵A1=A2=A2)Thus Cp=(2+4)×102=30μF

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