space between plates of a parallel plate capacitor is filled with dielectric whose dielectric constant varies with distance as per relation:
K(x) = K₀ + Bx ( B = constant )
the capacitance C of this capacitor would be related to its vacuum capacitance C₀ as per the relation ??

Question

space between plates of a parallel plate capacitor is filled with
dielectric whose dielectric constant varies with distance as per
relation:
K(x) = K0 + Bx ( B = constant )
the capacitance C of this capacitor would be related to its vacuum
capacitance C0 as per the relation ??

Vaibhav T. · Accepted Answer

Dear Student,

dC=K0+Bxε0Adx∫1dC=∫0ϕdxK0+Bxε0ALet K0+Bx=tBdx=dt∫1dC=1Bε0∫K0K0+BddtAt1C=1ABε0ln tK0K0+Bd1C=1ABε0ln K0+Bd-ln K01C=1ABε0lnK0+BdK0  
 1C0=ε0AdA=C0dε0  
 2from 1 & 2, we get,1C=ε0C0dBε0lnK0+BdK01C=1C0dBlnK0+BdK0C=Bdln1+BdK0C0

space between plates of a parallel plate capacitor is filled with dielectric whose dielectric constant varies with distance as per relation: K(x) = K0 + Bx ( B = constant ) the capacitance C of this capacitor would be related to its vacuum capacitance C0 as per the relation ??

space between plates of a parallel plate capacitor is filled with dielectric whose dielectric constant varies with distance as per relation:
K(x) = K₀ + Bx ( B = constant )
the capacitance C of this capacitor would be related to its vacuum capacitance C₀ as per the relation ??