Answer to Question #314603 in Physics for Marcus

Question

A parallel plate air capacitor has a capacitance of 5 F. What is the capacitance if the separation between the plates is decreased to one-half its original value while keeping all other factors constant?

Answer 1

The capacitance of parallel plate capacitor

$$C=\frac{\epsilon_0 A}{d}$$

$$C'=\frac{\epsilon_0 A}{d'}=\frac{\epsilon_0 A}{d/2}=2\times\frac{\epsilon_0 A}{d}=2C\\ =2\times \rm 5\: F=10\: F$$