Question

1 megabit computer memory chip contains many 63.0 fF capacitors. Each capacitor has a plate area of 17.0 ✕ 10^-12 m². Determine the plate separation of such a capacitor (assume a parallel-plate configuration). The order of magnitude of the diameter of an atom is 10^-10 m = 0.100 nm. Express the plate separation in nanometers.

Answer 1

As given in the question,

Capacitance: C = 63.0 fF = 6.3*10^-14 F

Area: A = 17*10^-12 m^2 = 1.7*10^-11 m^2

The formula for the capacitance,

C = (ε₀*ε_r*A) / d ,   where ε₀ = 8.85*10^-12

Assuming air is the dielectric then ε_r = 1

=> C = (ε₀*A) / d

=> d = (ε₀*A) / C

= (8.85*10^-12)*(1.710^-11) / 6.3*10^-14

= 2.39*10^-9 m

=> d = 2.39 nm