Question

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

Answer 1

The capacitance of parallel plate capacitor

$$C=\frac{\epsilon_0 A}{d}$$ $$C'=\frac{\epsilon_0 A'}{d}=\frac{\epsilon_0 A/2}{d}=\frac{1}{2}\times\frac{\epsilon_0 A}{d}=\frac{1}{2}C\\ =\frac{1}{2}\times \rm 5\: F=2.5\: F$$