The space between the plates of a parallel plate capacitor is filled with a ' dielectric ' whose dielectric constant varies with distance as for the relation : $\;K(x)=K_{0}+\lambda x\;$ ($\lambda\;$)=a constant . The capacitance C , of this capacitor , would be related to its ' vacuum ' capacitance $\;C_{0}\;$ as for the relation :

Question

$(a)\;\normalsize C=\large\frac{\lambda d} {ln(1+K_{0} \lambda d)} \;\normalsize C_{0}\qquad(b)\;\normalsize C=\large\frac{\lambda } {d\;.ln(1+K_{0} \lambda d)} \;\normalsize C_{0}\qquad(c)\;\normalsize C=\large\frac{\lambda d} {ln(1+\large\frac{\lambda d}{K_{0}} )} \;\normalsize C_{0}\qquad(d)\;\normalsize C=\large\frac{\lambda } {d\;.ln(1+\large\frac{K_{0}} {\lambda d})} \;\normalsize C_{0}$