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Question

A capacitor is formed by two square metal plates each of edge a=10 cm separated by a distance d=7 mm. Dielectrics of dielectric constant K1=8 and K2=4 are filled in the gap as shown in figure, what is the capacitance of this system? (ln2=0.7)


A
35.4 pF
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B
70.8 pF
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C
141.6 pF
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D
78 pF
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Solution

The correct option is B 70.8 pF
We know that for an arrangement shown in the question

Capacitance of the system is given by, C=ε0a2K1K2(K1K2)dlnK1K2

We have the values of corresponding variables as,
a=0.1 m
d=7×103
K1=8
K2=4

Substituting the given data we get, C=8.85×1012×0.1×8×4(84)7×103ln84

C=70.8 pF

Hence, option (b) is the correct answer.

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