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:
$K (x) = K_{o} + λ x (λ = a constant)$
The capacitance C, of the capacitor, would be related to its vacuum capacitance $C_{0}$ by the relation:

Question

Infinity Learn · Accepted Answer

Capacitance of capacitor with dielectric material $$=C0=$$ε$$0AddC=$$ε$$0(K0+$$λ$$x)Adx$$⇒$$1C=$$∫$$1dC$$⇒$$1C=$$∫$$0ddx$$ε$$0(K0+$$λ$$x)A$$⇒$$1C=1A$$ε$$0$$λ×[$$ln(K0+$$λ$$x)$$]$$0d$$⇒$$1C=1A$$ε$$0$$λ×[$$ln(K0+$$λ$$d)$$−$$ln(K0)$$]⇒$$C=A$$ε$$0$$λ$$ln(1+$$λ$$dK0)$$⇒$$C=$$λ$$dln(1+$$λ$$dK0)C0$$

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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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