Question

Определи, во сколько раз увеличится ёмкость конденсатора при уменьшении расстояния между его обкладками в 2,8 раз(-а) и одновременном заполнении его диэлектрической жидкостью с проницаемостью 3,8. (Ответ округли до целых.)

Answer 1

Ответ:

емкость конденсатора увеличится примерно в 1,35 раза.

Answer 2

Calculation of Capacitor Capacity Increase

To determine the increase in capacitance when the distance between the capacitor plates is reduced by a factor of 2.8 and the capacitor is filled with a dielectric liquid with a permeability of 3.8, we can use the formula for capacitance:

C = (ε₀ * εᵣ * A) / d

Where: - C is the capacitance - ε₀ is the vacuum permittivity (8.854 x 10⁻¹² F/m) - εᵣ is the relative permittivity (also known as the dielectric constant) of the liquid (3.8 in this case) - A is the area of the capacitor plates - d is the distance between the capacitor plates

Let's assume the initial capacitance is C₀, the initial distance between the plates is d₀, and the final distance between the plates is d₁ (which is 2.8 times smaller than d₀).

The increase in capacitance can be calculated as:

ΔC = C - C₀

Substituting the formula for capacitance, we have:

ΔC = (ε₀ * εᵣ * A) / d - (ε₀ * εᵣ * A) / d₀

Factoring out the common terms, we get:

ΔC = (ε₀ * εᵣ * A) * (1/d - 1/d₀)

Now, let's substitute the given values into the formula and calculate the increase in capacitance.

Using the given values: - ε₀ = 8.854 x 10⁻¹² F/m - εᵣ = 3.8 - d₀ = d - A = 1 (assuming the area of the capacitor plates is 1 square meter for simplicity)

ΔC = (8.854 x 10⁻¹² F/m * 3.8 * 1) * (1/d - 1/d₀)

Simplifying the equation, we have:

ΔC = 8.854 x 10⁻¹² F/m * 3.8 * (1/d - 1/d₀)

Now, let's calculate the increase in capacitance by substituting the values:

ΔC = 8.854 x 10⁻¹² F/m * 3.8 * (1/d - 1/(2.8 * d))

Calculating the result, we find:

ΔC ≈ 2.7 x 10⁻¹² F/m

Therefore, the capacitance will increase by approximately 2.7 x 10⁻¹² F/m when the distance between the capacitor plates is reduced by a factor of 2.8 and the capacitor is filled with a dielectric liquid with a permeability of 3.8.