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

Answer:

Plate separation of each capacitor is 101.132 °A

Explanation:

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

$C=\epsilon_{0}\frac{Area}{distance}$

clearing for distance:

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