Surge impedance values for cables are

Question

Examoogle · Accepted Answer

Option B: Lower than those of overhead lines

Explanation & Concepts:
The surge impedance (or characteristic impedance) of a transmission line is defined as $Z_c = \sqrt{\frac{L}{C}}$. Cables have significantly higher capacitance ($C$) due to the close proximity of conductors separated by thin dielectric insulation compared to the wide spacing of overhead lines, leading to a much lower surge impedance value.

Working Principle: In an overhead line, conductors are separated by air (dielectric constant $\approx 1$), resulting in low capacitance and high inductance per unit length. In contrast, cables utilize solid or liquid insulation with high permittivity, increasing capacitance significantly while reducing inductance. Since $Z_c \propto \sqrt{\frac{1}{C}}$, the increase in $C$ dominates, causing $Z_c$ to drop typically from 400-600 $\Omega$ for overhead lines to 30-50 $\Omega$ for cables.

Key Formulas: $Z_c = \sqrt{\frac{L}{C}}$ — Surge impedance of a lossless transmission line; $v = \frac{1}{\sqrt{LC}}$ — Velocity of electromagnetic wave propagation

Key Points: Overhead line surge impedance is typically $400 - 600 \ \Omega$.; Cable surge impedance is typically $30 - 50 \ \Omega$.; Higher capacitance in cables is due to the small distance between the conductor and the grounded sheath.

Advantages: Lower surge impedance in cables reduces the magnitude of voltage surges entering connected equipment.; Higher capacitance aids in maintaining voltage stability over shorter distances.

Disadvantages: High shunt capacitance leads to charging currents that limit the effective transmission length of cables.; Increased cable cost compared to overhead lines due to insulation requirements.

Applications: Underground power distribution in urban areas; Submarine power transmission

Additional Info: The permittivity of insulation materials ($\epsilon_r$) in cables is significantly higher than that of air ($\epsilon_r \approx 1$), which is the primary reason for the increased capacitance ($C = \frac{2\pi\epsilon}{\ln(D/d)}$).. Option A is incorrect as cables have much higher capacitance, reducing impedance. Option C is incorrect as the values differ by an order of magnitude.

Answer: B is correct — Surge impedance of cables is significantly lower than overhead lines due to high shunt capacitance.

Exam Tip: Remember that $Z_c$ is inversely proportional to $\sqrt{C}$; since cables are designed to have high capacitance per meter, they inherently possess lower surge impedance.

Examoogle · Answer

Option A: Higher than those of overhead lines

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Option C: In a same order is those of overhead line

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Option D: None of above

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