A capacitor is formed of two identical coaxial disks of diameter 28cm. The distance d between the disks is adjustable .
Calculate the capacitance of this capacitor at d=5mm.
What becomes the value of this capacitance if a glass sheet 5mm thick is inserted to fill the gap between the plates?(relative permittivity of glass Er=4)
C = κεoA/d
εo is a constant
make sure to convert units
To calculate the capacitance of a capacitor, you can use the formula:
C = (ε₀ * εᵣ * A) / d
Where:
C = Capacitance
ε₀ = Permittivity of free space (8.854 x 10⁻¹² F/m)
εᵣ = Relative permittivity of the material between the capacitor plates
A = Area of the plates
d = Distance between the plates
In this case, we are given the diameter of the capacitor plates, which can be used to calculate the area.
First, let's calculate the area of each disk:
Radius (r) = Diameter / 2 = 28 cm / 2 = 14 cm = 0.14 m
Area (A) = π * r² = π * (0.14 m)²
Next, we can calculate the capacitance at d = 5 mm:
d = 5 mm = 0.005 m
Now we substitute the values into the capacitance formula:
C = (ε₀ * εᵣ * A) / d
Since we are given the relative permittivity of the glass (εᵣ = 4), we can calculate the capacitance with the glass sheet in place.
Let's calculate the capacitance with the glass sheet inserted:
C with glass = (ε₀ * εᵣ * A) / d
Inserting the values into the formula, we get:
C with glass = (8.854 x 10⁻¹² F/m * 4 * π * (0.14 m)²) / (0.005 m)
Now you can use a calculator to find the numerical value of the capacitance.