Answer to Question #293071 in Electric Circuits for Nene

Question

Calculate the capacitance of a capacitor whose plates are 25cm x 4.0 cm and are separated by a 2.0mm air gap.

Answer 1

The formula to calculate the capacitance with dielectric is

$C=k\epsilon_0 \frac{A}{d} \\ \text{} \\ \text{where k is the dielectric constant, }\epsilon_0 \\ \text{is the absolute permittivity, A is the} \\ \text{area of the plates, and d} \\ \text{is the distance between them.}$

Since k = 1.00059 for air and $\epsilon_0$= 8.854 X 10^-12 F/m, we proceed to substitute and we find:

$C = (1.00059)(8.854\times 10^{-12}\frac{F}{\cancel{m}})\frac{(0.25\cancel{\,m})(40.0 \cancel{\,mm})}{2.0 \cancel{\,mm}} \\ \text{} \\ \therefore C = 4.43\times 10^{-11}\,F$

In conclusion, the capacitance for this array is 4.43 X 10^-11 F.