The surge impedance of transmission line is represented by (l is line series inductance per length,

Question

The surge impedance of transmission line is represented by (l is line series inductance per length, c is distributed capacitance per length)

Examoogle · Accepted Answer

$\sqrt{\frac{l}{c}}$

Explanation: The surge impedance ($Z_s$) of a transmission line is defined as the characteristic impedance of a lossless transmission line. It is determined by the ratio of the series inductance per unit length ($l$) to the shunt capacitance per unit length ($c$), expressed as $\sqrt{\frac{l}{c}}$.

Working Principle: In a lossless line, the propagation constant is determined by the interaction between the magnetic field energy stored in the series inductance and the electric field energy stored in the shunt capacitance. When the line is terminated with its surge impedance, the traveling wave experiences no reflections, and the voltage to current ratio is maintained at the value of $\sqrt{\frac{l}{c}}$. This is also known as the natural impedance of the line.

Key Formulas: $Z_s = \sqrt{\frac{l}{c}}$ — Surge Impedance formula; $Z_0 = \sqrt{\frac{r + j\omega l}{g + j\omega c}}$ — Characteristic Impedance of a general line

Key Points: Surge impedance is independent of line length.; For overhead lines, the surge impedance is typically between 300 to 500 ohms.; For underground cables, the surge impedance is much lower, typically 30 to 50 ohms, due to higher shunt capacitance.; When a line is loaded at its surge impedance loading (SIL), the reactive power generated equals the reactive power absorbed.

Advantages: Useful for calculating SIL (Surge Impedance Loading).; Essential for transmission line insulation coordination.

Disadvantages: Applies strictly only to lossless lines; real lines have resistance and leakage.; Does not account for frequency-dependent effects in actual power systems.

Applications: Power system stability studies.; Insulation coordination and protection of equipment from switching surges.

Additional Info: Option A, B, and C are mathematically incorrect as they introduce scaling factors not present in the fundamental physics of wave propagation.. SIL = $\frac{V_{LL}^2}{Z_s}$ represents the power level at which the line delivers reactive power to the system.

Answer: D is correct — The surge impedance is defined as the square root of the ratio of the series inductance to the shunt capacitance, represented as $\sqrt{\frac{l}{c}}$.

Exam Tip: Always remember that underground cables have significantly higher capacitance than overhead lines, leading to a much lower surge impedance.

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