Question

Плоский воздушный конденсатор зарядили до 200В, отключили от сети и присоединили параллельно к незаряженному конденсатору таких же размеров, но с диэлектриком. найти диэлектрическую проницаемость этого диэлектрика, если напряжение на батарее оказалось 25В.

Answer 1

Емкость конденсатора связана с напряжением и зарядом
U=Q/C0,
находим заряд
Q=200·C0
Если в конденсаторе есть диэлектрик, то его емкость
С= ε·С0
Если конденсаторы соединены параллельно, то их суммарную емкость необходимо сложить
C0+ ε·С0=(1+ ε)·С0
Можно определить значение заряда
Q=25·(1+ ε)·С0
поскольку заряд не менялся, то эти выражение равны
200·C0=25·(1+ ε)·С0
или
200=25·(1+ ε)
ε = 7

Answer 2

Calculation of the Dielectric Permittivity

To find the dielectric permittivity of the dielectric material, we can use the concept of capacitance and the formula for the capacitance of a parallel plate capacitor.

Let's assume that the initial capacitance of the charged capacitor (with air as the dielectric) is C1, and the capacitance of the uncharged capacitor (with the dielectric material) is C2. The voltage across the charged capacitor is V1 = 200V, and the voltage across the battery is V2 = 25V.

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

C = (ε₀ * ε * A) / d

Where: - C is the capacitance - ε₀ is the vacuum permittivity (8.854 x 10^-12 F/m) - ε is the dielectric permittivity - A is the area of the plates - d is the distance between the plates

Since the two capacitors are connected in parallel, the total capacitance (C_total) is the sum of the individual capacitances:

C_total = C1 + C2

We can rearrange the formula for capacitance to solve for the dielectric permittivity (ε):

ε = (C * d) / (ε₀ * A)

To find the dielectric permittivity, we need to know the area of the plates and the distance between them. Unfortunately, the provided information does not include these values. Therefore, we cannot calculate the dielectric permittivity without this information.

If you have the values for the area and distance, please provide them, and I will be happy to help you calculate the dielectric permittivity.