Question

You need to construct a 100 pF capacitor for a science project. You plan to cut two L * L metal squares and insert small spacers between their corners. The thinnest spacers you have are 0.20 mm thick. What is the proper value of L?

Short answer

The value of$L$is$4.75cm$

Step-by-step solution

Given information

We have given that the thinnest spacers are $0.20mm$thick.

We need to find that the proper value of $L$.

Capacitance of capacitor

The capacitance of any parallel-plate capacitor is given as

$C={\in }_0\frac{A}{d}$

For square plates, the area is

$A=L^2$

By substituting the capacitance will be given as

$C={\in }_0\frac{L^2}{d}$

This allows us to express the length as

$L=\sqrt{\frac{dC}{\in }}$

Using the numerical values we get

$L=\sqrt{\frac{2·{10}^{-4}·1·{10}^{-10}}{8.85·{10}^{-12}}}=4.75cm$