Question

A 1-megabit computer memory chip contains many 27 fF capacitors. Each capacitor has a plate area of 3.09 × 10−11 m 2 . Determine the plate separation of such a capacitor (assume an empty parallel-plate configuration). The characteristic atomic diameter is 10−10 m = 1 ˚A, and the permittivity of a vacuum is 8.8542 × 10−12 C 2 /N · m2 . Answer in units of ˚A.

Answer 1

Plate separation of each capacitor is 101.132 °A

Step-by-step explanation:

The formula to calculate the capacitance in empty space as a function of distance (square parallel plates) is:

`C=\epsilon_(0)(Area)/(distance)`

clearing for distance:

`distance=\epsilon_0 (Area)/(Capacitance) \\\\\epsilon_0=8.8542(10)^(-12)C^2/Nm\\\\Area=3.09(10)^(-11)m^2\\Capacitance=27(10)^(-15)F\\\\Replacing\\\\distance=(8.8542(10)^(-12)*3.09(10)^(-11))/(27(10)^(-15)) =1.0133(10)^(-8)m\\\\In A\\distance= 101.132 A`