The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation:K(x)=Ko+λx(λ=a constant )The capacitance C, of the capacitor, would be related to its vacuum capacitance C0 by the relation:
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a
C=λdln1+KoλdCo
b
C=λd·ln1+KoλdCo
c
C=λdln1+λd/K0Co
d
C=λd·ln1+K0/λdCo
answer is C.
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Detailed Solution
Capacitance of capacitor with dielectric material =C0=ε0AddC=ε0(K0+λx)Adx⇒1C=∫1dC⇒1C=∫0ddxε0(K0+λx)A⇒1C=1Aε0λ×[ln(K0+λx)]0d⇒1C=1Aε0λ×[ln(K0+λd)−ln(K0)]⇒C=Aε0λln(1+λdK0)⇒C=λdln(1+λdK0)C0