To determine the maximum voltage that a coaxial cable can handle without experiencing corona discharge, we need to consider several factors, including the geometry of the cable and the dielectric properties of the materials involved. Let's break this down step by step.
Understanding the Structure
The coaxial cable consists of an inner conductor with a radius of a = 3 mm and an outer conductor with a radius of c = 12 mm. Between these conductors, there are two concentric layers of dielectric materials. The first dielectric layer extends from the inner conductor to a radius of b = 6 mm.
Dielectric Properties
The dielectric constants and breakdown strengths for the two layers are as follows:
- First dielectric (between a and b): Relative permittivity Ɛ r1 = 5, Breakdown strength E S1 = 400 kV/cm
- Second dielectric (between b and c): Relative permittivity Ɛ r2 = 8, Breakdown strength E S2 = 100 kV/cm
Calculating Maximum Voltage
The maximum voltage for each dielectric layer can be calculated using the formula:
U max = E S × d
Where:
- U max is the maximum voltage.
- E S is the breakdown strength of the dielectric.
- d is the thickness of the dielectric layer.
First Dielectric Layer
The thickness of the first dielectric layer is:
d1 = b - a = 6 mm - 3 mm = 3 mm
Now, converting this to centimeters for consistency with the breakdown strength:
d1 = 0.3 cm
Using the breakdown strength for the first dielectric:
U max1 = E S1 × d1 = 400 kV/cm × 0.3 cm = 120 kV
Second Dielectric Layer
The thickness of the second dielectric layer is:
d2 = c - b = 12 mm - 6 mm = 6 mm
Again, converting this to centimeters:
d2 = 0.6 cm
Using the breakdown strength for the second dielectric:
U max2 = E S2 × d2 = 100 kV/cm × 0.6 cm = 60 kV
Final Calculation
The overall maximum voltage that the coaxial cable can handle without corona discharge is determined by the lower of the two calculated maximum voltages:
U max = min(U max1, U max2) = min(120 kV, 60 kV) = 60 kV
Considering the Result
It seems there might be a misunderstanding in the provided result of U max = 108.13 kV. Based on the calculations, the maximum voltage without corona effect should be 60 kV. If you have additional parameters or conditions that might affect this calculation, please share them for further analysis.
In summary, the maximum voltage that the coaxial cable can withstand without experiencing corona discharge is primarily determined by the breakdown strength of the dielectric materials and their respective thicknesses. In this case, the limiting factor is the second dielectric layer, resulting in a maximum voltage of 60 kV.
