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To obtain the minimum value of stress in cables, the ratio (R/r) should be
13
718
96
5
718
To minimize the maximum stress in a single-core underground cable, the ratio of the sheath radius (R) to the conductor radius (r) should be equal to the base of the natural logarithm, which is approximately 2.718.
To minimize the maximum stress in a single-core underground cable, the ratio of the sheath radius (R) to the conductor radius (r) should be equal to the base of the natural logarithm, which is approximately 2.718.
gxтАЛ=xln(R/r)VтАЛ тАФ Electric stress at radius x
gmaxтАЛ=rln(R/r)VтАЛ тАФ Maximum stress at conductor surface
The electric stress at any point x from the center of a single-core cable is given by gxтАЛ=xln(R/r)VтАЛ. To minimize the maximum stress at the conductor surface (where x = r), we differentiate gmaxтАЛ with respect to r and set it to zero. This optimization yields the condition R/r=eтЙИ2.718.
The condition R/r=e ensures the most efficient use of insulation material.
If the ratio R/r is kept at 2.718, the stress at the conductor surface is minimized for a given conductor size.
This calculation assumes a homogeneous dielectric material.
Reduces the thickness of insulation required for a specific voltage rating.
Optimizes the overall diameter of the cable.
Often leads to a very thin conductor for high-voltage cables, causing mechanical strength issues.
May result in a conductor radius that is too small for the required current carrying capacity.
Design of high-voltage single-core cables.
Optimization of dielectric stress distribution in power transmission cables.
The numerical value 2.718 represents the mathematical constant 'e'.
In practice, the ratio is often chosen to be larger than 2.718 to accommodate thermal and mechanical constraints.
B is correct тАФ The optimal ratio for minimizing stress in a single-core cable is the mathematical constant eтЙИ2.718.
Always verify if the question asks for the theoretical minimum stress ratio (e) or practical constraints, as industrial cables rarely use exactly 2.718 due to current capacity requirements.