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A budding electronics hobbyist wants to make a simple 1.0-nF capacitor for tuning her crystal radio, using two sheets of aluminum foil as plates, with a few sheets of paper between them as a dielectric. The paper has a dielectric constant of 3.0, and the thickness of one sheet of it is 0.20 mm. (a) If the sheets of paper measure 22×28cm and she cuts the aluminum foil to the same dimensions, how many sheets of paper should she use between her plates to get the proper capacitance? (b) Suppose for convenience she wants to use a single sheet of poster board, with the same dielectric constant but a thickness of 12.0 mm, instead of the paper. What area of aluminum foil will she need for her plates to get her 1.0 nF of capacitance? (c) Suppose she goes high-tech and finds a sheet of Teflon of the same thickness as the poster board to use as a dielectric. Will she need a larger or smaller area of Teflon than of poster board? Explain.

Respuesta :

MrRoyal

Answer:

a. 8 sheets of paper is needed between her plates to get the proper capacitance

b. Area of Aluminum Foil needed = 0.45m²

c. To keep a 1.0-nF, a larger area of Teflon is required.

Explanation:

a.

First, we need to calculate the distance between two plates.

This is given by

d = Kε0A/C

Where

K = 3

ε0 = Physical Constant = 8.854 * 10^-12 C²/Nm²

A = Area = 22 * 28 = 616cm² = 0.0616m²

C = 1.0-nF = 1 * 10^-12F

So, d = (3 * 8.854 * 10^-12 C²/Nm² * 0.0616) / (1 * 10^-12F)

d = 1.64 * 10^-3m

d = 1.64mm

Now, that the distance has been solved.

The Number of Sheets, N is given by

N = d/d,sheet where d, sheet =the sheet thickness = 0.2mm

N = 1.64/0.2

N = 8.2

N = 8 sheets --- Approximated

b.

Here, she's changed the diameter of the sheets to 12mm

Well make use of the formula in (a) above

Using d = Kε0A/C

Where

d = 12 * 10^-3m

Other constraints remain unchanged

Make A the subject of formula

A = dC/Kε0

A = (12 * 10^-3m * 1 * 10^-12F)/(3 * 8.854 * 10^-12 C²/Nm²)

A= 0.45m²

c. From (b) above

A ∝ 1/K

As the dielectric constant increase, the area decreases

The dielectric constant of a Teflon is 2.1

This means that if she used a Teflon instead, the area will be larger.

So, to keep a 1.0-nF, a larger area of Teflon is required.

The number of sheets of paper should she use between her plates to get the proper capacitance is; 8 sheets

What is the effect of the dielectric constant on the area?

A) The distance between the two plates is given by the formula;

d = Kε₀A/C

Where;

K is dielectric constant = 3

ε₀ is permittivity of vacuum = 8.854 × 10⁻¹² C²/Nm²

A is Area = 22 × 28 = 616cm² = 0.0616m²

C = 1.0 nF = 1 × 10⁻⁹ F

Thus;

d = (3 × 8.854 × 10⁻¹² C²/Nm² × 0.0616)/(1 × 10⁻⁹ F)

d = 1.64 * 10⁻³ m = 1.64mm

The Number of Sheets, N is gotten from the expression;

N = d/d_sheet

where;

d  is distance

d_sheet is the sheet thickness = 0.2 mm

Thus;

N = 1.64/0.2

N ≈ 8 sheets

B) Now, the thickness of the sheets has been changed to 12mm = 12 × 10⁻³ m

Thus, Area is;

A = dC/(Kε₀)

A = (12 * 10⁻³ × 1 × 10⁻⁹)/(3 × 8.854 × 10⁻¹²)

A = 0.45m²

C) The relationship between Area and dielectric constant is; A ∝ 1/K

Thus, as the dielectric constant increases, the area will be decreasing and vice versa.

Now, the dielectric constant of a Teflon is 2.1 and this is lesser than that of the aluminium and so if she used teflon, the area will be larger.

Read more about dielectric constant at; https://brainly.com/question/27017570?source=archive

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