Question

. A sheet of paper 4.0cm and 1.5x10-3cm thick between metal foil of the same width is used to make a 2.0μF capacitor. If the dielectric constant (relative permittivity) of the paper is 2.5, what length of paper is required?​

Answer 1

The length of paper required is 5.9 cm.

Step-by-step explanation:

To find the length of the paper required to make the capacitor, we can use the formula for the capacitance of a parallel plate capacitor with a dielectric material:

C = (K * ε₀ * A) / d

Where C is the capacitance, K is the dielectric constant, ε₀ is the permittivity of free space, A is the area of one plate, and d is the distance between the plates.

Rearranging the formula to solve for the length of the paper gives:

d = (K * ε₀ * A) / C

Substituting the given values:

d = (2.5 * 8.85 × 10-12 F/m * (4.0 cm * 1.5 x 10-3 cm)) / (2.0 x 10-6 F)

= 0.059 m

= 5.9 cm

Therefore, a length of 5.9 cm of paper is required to make the 2.0 μF capacitor.