Question

Space between plates is filled by two dielectrics $K_1\&K_2,{\frac{2}{3}}^{rd}$ part is filled by $K_1\&{\frac{1}{3}}^{rd}$ is filled by $K_2$, find effective dielectric constant. Area of the plates is $A$.

• A. $\frac{2K_1+K_2}{3}$
• B. $\frac{K_1+2K_2}{3}$
• C. $\frac{3K_1+K_2}{4}$
• D. $\frac{K_1+3K_2}{4}$

Answer 1

The correct option is A $\frac{2K_1+K_2}{3}$


Both capacitors connected parallel. So

$C_{eff}=C_1+C_2$

$=\frac{{ϵ}_0\frac{2A}{3}{K}_1}{d}+\frac{{ϵ}_0\frac{A}{3}{K}_2}{d}$

$\left(\frac{{ϵ}_{0}A}{d}\right)K_{eff}=\frac{{ϵ}_{0}A}{d}(\frac{2K_1}{3}+\frac{K_2}{3})$

$K_{eff}=\frac{2K_1+K_2}{3}$