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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 F
Initial capacitance is given as C=10μF
C=ε0Ad=10μF
New arrangement acts as two capacitors C1 and C2 connected in parallel.
Thus capacitance of each part C1=k1ε0A1d and C2=k2ε0A2d
Equivalent 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

63539_11125_ans_b5a3b4fce9eb4a57a50fae32f3133ad2.png

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