Question

Consider a parallel plate capacitor having plates of area 1.65 cm² that are separated by 0.028 mm of neoprene rubber. You may assume the rubber has a dielectric constant -κ = 6.7. What is the capacitance of the capacitor?

Answer 1

The capacitance of a parallel plate capacitor can be calculated using the formula C = ε0 εrA/d, where ε0 is the vacuum permittivity, εr is the dielectric constant, A is the area of the plates, and d is the separation between the plates.

Step-by-step explanation:

The question asks for the capacitance of a parallel plate capacitor with known area and the dielectric material between its plates.

To calculate the capacitance (C) of a parallel plate capacitor, the formula is:

C = ε0 εrA/d

where:

ε0 is the vacuum permittivity (≈ 8.854 x 10-12 F/m),

εr is the relative permittivity or dielectric constant of neoprene rubber (6.7 in this case),

A is the area of the plates (converted to square meters), and

d is the distance between the plates in meters.

First, convert the area from cm² to m²:

1.65 cm² = 1.65 x 10-4 m²

Next, convert the distance from mm to m:

0.028 mm = 2.8 x 10-5 m

Using these values, the capacitance can be calculated as:

C = (8.854 x 10-12 F/m) x 6.7 x (1.65 x 10-4 m²) / (2.8 x 10-5 m)

After calculating, the capacitance C of the capacitor is determined.