# Plate capacitor Formula

The capacitance of a parallel plate capacitor depends on the area of the plates A and their separation d.

Capacitance = (relative permittivity)* (permittivity of space) * (Plates area) / (distance between plates)

The equation is:

C = k ϵ A/d

Where:

C: Capacitance

A: Area of the plates

d: distance between plates

k: relative permittivity

ϵ: permittivity of space

Plate capacitor Formula Questions:

1) A plate capacitor filled with air is formed by to plates separated by 1 cm. The plates have an area of 0.16 m^{2}. What is its capacitance?

Answer:

From the plate capacitance formula, we substitute the permittivity, equals to one for air, the area and distance:

C = k ϵ A/d = (8.854 *10^{(-12)} F/m) * 0.16 m^{2} / 0.01 m

C = 1.41*10^{(-10)} F = 0.14 nF

2) A plate capacitor filled with paper is formed by to plates separated by 2 cm. The plates have an area of 0.48 m^{2}. What is its capacitance?

Answer:

From the plate capacitance formula, we substitute the permittivity, equals to 3.85 for paper, the area and distance:

C = k ϵ A/d = (8.854 *10^{(-12)} F/m) (3.85) * 0.48 m^{2} / 0.02 m

C = 8.18*10^{(-10)} F = 0.81 nF

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