Question

Consider a parallel plate capacitor having plates of area 1.6 cm² that are separated by 0.016 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

To find the capacitance of a parallel plate capacitor with plates of area 1.6 cm², separated by 0.016 mm of neoprene rubber (dielectric constant 6.7), use the formula C = κε_0(A/d). Upon inserting the given values into this formula, you can calculate the capacitor's capacitance.

Step-by-step explanation:

The capacitance of a parallel plate capacitor can be found using the formula:

C = κε_0(A/d)

Where C is the capacitance, κ is the dielectric constant, ε_0 is the vacuum permittivity (8.854 x 10-12 C2/N·m2), A is the area of one of the plates, and d is the separation between the plates.

In this case:

• The area A is 1.6 cm² which is 1.6 x 10-4 m².
• The separation d is 0.016 mm, or 0.016 x 10-3 m.
• The dielectric constant κ for neoprene rubber is 6.7.

Substituting these values into the capacitance formula gives:

C = 6.7 x 8.854 x 10-12 x (1.6 x 10-4)/(0.016 x 10-3)

Simplifying this will give the capacitance of the parallel plate capacitor.