In a cable of conductor diameter d and overall diameter with dielectric material D, the maximum dielectric str

Question

In a cable of conductor diameter d and overall diameter with dielectric material D, the maximum dielectric stress

Examoogle · Accepted Answer

The correct answer is Option B: Occurs at the conductor surface and is proportional to $1/d$. In a single-core underground cable, the dielectric stress (electric field intensity) is not uniform. It reaches its maximum value at the conductor surface (where the radius $r$ is minimum) and decreases as we move towards the sheath (where the radius is maximum).

Step-by-Step Solution & Concepts:
In a single-core underground cable, the dielectric stress (electric field intensity) is not uniform. It reaches its maximum value at the conductor surface (where the radius $r$ is minimum) and decreases as we move towards the sheath (where the radius is maximum).

Working Principle: The electric stress $g$ at any radius $r$ from the center of a conductor is given by $g = \frac{V}{r \ln(\frac{D}{d})}$. Since $V$ and the term $\ln(\frac{D}{d})$ are constants for a fixed cable design, the stress $g$ is inversely proportional to the radius $r$. At the conductor surface, $r = \frac{d}{2}$, resulting in the maximum stress $g_{max} = \frac{2V}{d \ln(\frac{D}{d})}$, which shows that $g_{max} \propto \frac{1}{d}$.

Key Formulas: $g_r = \frac{V}{r \ln(D/d)}$ — Dielectric stress at any radius $r$; $g_{max} = \frac{2V}{d \ln(D/d)}$ — Maximum dielectric stress at conductor surface ($r = d/2$)

Key Points: Dielectric stress is inversely proportional to the distance from the center of the conductor.; Maximum stress occurs at the conductor surface where the radius is smallest.; Minimum stress occurs at the dielectric surface (sheath) where the radius is largest.; To minimize $g_{max}$, the ratio $D/d$ is usually optimized, typically around $e \approx 2.718$.

Advantages: Calculations help in determining the required insulation thickness.; Ensures cable longevity by preventing dielectric breakdown at the conductor interface.

Disadvantages: Non-uniform stress distribution leads to inefficient utilization of insulating material.; Higher conductor diameters lead to lower stress concentrations.

Applications: Design of HV and EHV underground cables.; Grading of cables using capacitive or inter-sheath methods.

Additional Info: The stress is maximum at the conductor surface because the flux lines are most densely packed there.. Option B is correct because $g_{max} \propto 1/d$. If $d$ increases, the surface area increases, distributing the same potential over a larger perimeter, thus reducing stress.

Answer: B is correct — The maximum dielectric stress occurs at the conductor surface and is inversely proportional to the conductor diameter $d$.

Exam Tip: Remember that in high voltage cables, stress grading is employed to make the electric field distribution more uniform across the dielectric.

Examoogle · Answer

Option A: Occurs at the conductor surface and is proportional to $d$

Examoogle · Answer

Option C: Occurs at the middle of dielectric and is proportional to $1/D$

Examoogle · Answer

Option D: Occurs at the outer surface of dielectric and is proportional to $D$

Correct Answer

Discussion (0)

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)

Correct Answer

Related Questions

Discussion (0)