Question

Consider two air-filled parallel-plate capacitors with circular plates. Capacitor 1 has a distance between plates d and plate radius R. Capacitor 2 has a distance between plates 2d and plate radius R/2.
If the capacitance of capacitor 1 is C, then the capacitance of capacitor 2 is?

Answer 1

Answer:

1/8 x C

Explanation:

The capacitance of parallel plate capacitor

= ε₀ A /d where A is area of plate and d is distance between plate.

for capacitor 1

C =  ε₀ A /d

For capacitor 2

radius = R/2

Area = A / 4

Capacitance

= ε₀ (A/4) x ( 1 / 2d )

= ( 1 / 8) x (ε₀ A /d)

= 1/8 x C