# Problem Create a Plate Capacitor with a Certain Capacitance

**Level 2**requires school mathematics. Suitable for pupils.

*Capacitors are characterized by the electrical capacitance. It tells you how good a capacitor can "store" electric charge. The goal of modern technology is usually to produce the smallest possible capacitors with the largest possible capacitance so that such a component also fits into your smartphone.*

You want to have a plate capacitor which has a capacitance of \( C = 0.5 \, \text{nF} \) (nano farad). The area of a capacitor plate is given as \( A = 12 \, \text{cm}^2 \).

How large do you have to choose the distance \( d \) of the plates to reach this capacitance?

What else can you do to achieve the specified capacitance when the plate distance is set to \( d = 1.5 \, \text{mm} \)?

## Solution tips

All you need is the formula for the capacitance of a plate capacitor.

## Exercise solutions

## Solution for (a)

**Formel für die Kapazität eines Plattenkondensators**

**Plattenabstand mittels Kapazität**

**Plattenabstand konkret berechnet**

~&=~ 2.1 \cdot 10^{-5} \, \text{m} ~=~ 0.021 \, \mathrm{mm} \end{align} $$

## Solution for (b)

**Relative Permittivität mittels Kapazität**

**Relative Permittivität konkret berechnet**

~&\approx~ 89 \end{align} $$