Question

площадь пластин плоского конденсатора увеличили в 2 раза. как надо изменить расстояние между пластинами чтобы электроёмкость конденсатора увеличилась в 8 раз

Answer 1

Ответ:

емкость конденсатора прямо (прямая пропорциональность) зависит от площади пластин

и обратно (обратная пропорциональность) зависит от расстояния между пластинами.

значит расстояние надо сократить в 4 раза, если сначала увеличили площадь в 2 раза

Объяснение:

Answer 2

Calculation of Capacitance Increase

To calculate how the distance between the plates of a flat capacitor should change in order to increase the capacitance by a factor of 8 when the area of the plates is increased by a factor of 2, we can use the formula for the capacitance of a parallel-plate capacitor:

C = (ε₀ * A) / d

Where: - C is the capacitance of the capacitor - ε₀ is the permittivity of free space (a constant) - A is the area of the plates - d is the distance between the plates

Let's assume the initial capacitance is C₁ and the initial distance between the plates is d₁. After increasing the area of the plates by a factor of 2, the new area becomes 2A. We want to find the new distance between the plates, which we'll call d₂, that will result in a capacitance increase of 8 times the initial capacitance.

Using the formula for capacitance, we can set up the following equation:

(ε₀ * 2A) / d₂ = 8 * [(ε₀ * A) / d₁]

Simplifying the equation, we get:

2A / d₂ = 8 * (A / d₁)

Now, we can solve for d₂:

d₂ = (2A * d₁) / (8A) = d₁ / 4

Therefore, to increase the capacitance by a factor of 8, the distance between the plates should be reduced to one-fourth of its initial value.

Answer

To summarize, if the area of the plates of a flat capacitor is increased by a factor of 2, the distance between the plates should be reduced to one-fourth of its initial value in order to increase the capacitance by a factor of 8.

Please note that the calculations above are based on the assumption of a parallel-plate capacitor and the formula for capacitance in that specific configuration. Other types of capacitors may have different formulas and considerations.