Question

Как изменится электроемкость плоского воздушного конденсатора при уменьшении расстояния между его пластинами в 4 раза и введении между пластинами диэлектрика с диэлектрической проницаемостью, равной 2? Варианты ответов: 1) увеличится в 8 раз 2) увеличится в 2 раза 3) уменьшится в 2 раза 4) не изменится

Answer 1

Увеличится в 8  раз

потому что C=ε*εo*S/d

Answer 2

Увеличится в 8  раз

потому что C=ε*εo*S/d

Answer 3

Understanding the Change in Capacitance of a Parallel Plate Air Capacitor

When the distance between the plates of a parallel plate air capacitor is reduced by a factor of 4 and a dielectric with a dielectric constant of 2 is introduced between the plates, the capacitance of the capacitor will change. Let's explore how this change occurs.

Calculation of the Change in Capacitance

The capacitance of a parallel plate capacitor is given by the formula:

C = (ε * A) / d

Where: - C = capacitance - ε = permittivity of the material between the plates - A = area of the plates - d = distance between the plates

When a dielectric material is introduced between the plates, the capacitance becomes:

C' = (k * ε * A) / d

Where: - k = relative permittivity or dielectric constant of the material

Change in Capacitance

1. Initial Capacitance (C): - Let's assume the initial distance between the plates is d. - The initial capacitance C is given by the formula C = (ε * A) / d.

2. New Capacitance with Reduced Distance: - When the distance is reduced by a factor of 4, the new distance becomes d/4. - The new capacitance without the dielectric becomes C' = (ε * A) / (d/4) = 4 * (ε * A) / d.

3. New Capacitance with Dielectric: - When a dielectric with a dielectric constant of 2 is introduced, the new capacitance becomes C'' = (k * ε * A) / (d/4) = 8 * (ε * A) / d.

Conclusion

- The capacitance of the parallel plate air capacitor will increase by 8 times when the distance between its plates is reduced by 4 times and a dielectric with a dielectric constant of 2 is introduced between the plates.

This conclusion is supported by the formula for the capacitance of a parallel plate capacitor with and without a dielectric, as well as the principles of dielectric materials and their impact on capacitance.

Feel free to ask if you have further questions or need additional clarification!