A parallel plate capacitor is of area $6\, cm^2$ and a separation $3\, mm$. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants $K_1 = 10, K_2 = 12$ and $K_3 = 14$. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be
JEE MAIN 2019, Diffcult
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$\mathrm{C}_{\mathrm{net}}=\mathrm{C}_{1}+\mathrm{C}_{2}+\mathrm{C}_{3}$
$\frac{\mathrm{k} \mathrm{AE}_{\mathrm{o}}}{\mathrm{d}}=\mathrm{k}_{1}\left(\frac{\mathrm{A}}{3}\right) \frac{\mathrm{E}_{\mathrm{o}}}{\mathrm{d}}+\mathrm{k}_{2}\left(\frac{\mathrm{A}}{3}\right) \frac{\mathrm{E}_{\mathrm{o}}}{\mathrm{d}}+\mathrm{k}_{3}\left(\frac{\mathrm{A}}{3}\right) \frac{\mathrm{E}_{\mathrm{o}}}{\mathrm{d}}$
$\mathrm{k}=\frac{\mathrm{k}_{1}+\mathrm{k}_{2}+\mathrm{k}_{3}}{3}=12$
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