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A parallel plate condenser with plate area A and separation d is filled with dielectrics as shown in fig. The dielectric constants are K1 and K2 respectively. The capacitance will be

a
ε0AdK1+K2
b
ε0AdK1+K2K1K2
c
2ε0AdK1K2K1+K2
d
2ε0AdK1+K2K1K2

detailed solution

Correct option is C

The combination is equivalent to two capacitors in series, each with plate area A and separation d / 2.C1=K1ε0A(d/2)=2K1ε0AdC2=K2ε0A(d/2)=2K2ε0AdThe equivalent capacitance C is given by1C=1C1+1C2∴ 1C=d2K1ε0A+d2K2ε0A=d2ε0A1K1+1K2=d2ε0AK1+K2K1K2or     C=2ε0AdK1K2K1+K2

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