GATE EC 2016 Set 3 Q38 — Electronic Devices

Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator materials $X$ (of thickness $t_1 = 1$ nm and dielectric constant $\varepsilon_1=4$) and $Y$ (of thickness $t_2 = 3$ nm and dielectric constant $\varepsilon_2 = 20$). The capacitor in Figure II has only insulator material $X$ of thickness $t_{Eq}$. If the capacitors are of equal capacitance, then the value of $t_{Eq}$ (in nm) is _________