Question

The capacitance of a parallel-plate capacitor is 5 𝐹 when air is in between the plates and 32 𝐹 when the space is filled with a piece of plastic. What is the dielectric constant of the plastic?

Answer 1

The initial capacitance of an air-filled parallel-plate capacitor can be written as follows:

$$C_i=\dfrac{\epsilon_0A}{d}.$$

The final capacitance of the parallel-plate capacitor filled with a piece of plastic can be written as follows:

$$C_f=\dfrac{\kappa\epsilon_0A}{d}.$$

Let's divide $C_f$ by $C_i$:

$$\kappa=\dfrac{C_f}{C_i}=\dfrac{32\ F}{5\ F}=6.4.$$