The relation between traveling voltage wave and current wave is given as

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Examoogle · Accepted Answer

The correct answer is Option B: $\frac{e}{i} = \sqrt{\frac{L}{C}}$. The ratio of voltage ($e$) to current ($i$) in a traveling wave along a lossless transmission line is defined as the surge impedance or characteristic impedance ($Z_0$) of the line. This value is determined solely by the line's distributed parameters, inductance ($L$) and capacitance ($C$), and is independent of the line length.

Step-by-Step Solution & Concepts:
The ratio of voltage ($e$) to current ($i$) in a traveling wave along a lossless transmission line is defined as the surge impedance or characteristic impedance ($Z_0$) of the line. This value is determined solely by the line's distributed parameters, inductance ($L$) and capacitance ($C$), and is independent of the line length.

Working Principle: When a voltage surge propagates on a lossless line, the wavefront follows the wave equation derived from Maxwell's equations. The ratio of the electric field energy storage to the magnetic field energy storage determines the surge impedance. Mathematically, for a lossless line, the characteristic impedance is given by the square root of the ratio of inductance per unit length to capacitance per unit length.

Key Formulas: $Z_0 = \frac{e}{i} = \sqrt{\frac{L}{C}}$ — Definition of surge impedance for a lossless transmission line; $v = \frac{1}{\sqrt{LC}}$ — Velocity of the traveling wave

Key Points: Surge impedance for an overhead transmission line is typically in the range of 400–500 $\Omega$.; For underground cables, the surge impedance is significantly lower, typically 40–60 $\Omega$, due to high shunt capacitance.; The surge impedance is purely resistive for a lossless line.

Advantages: Useful for calculating voltage and current reflections at junctions.; Essential for insulation coordination and lightning protection design.

Disadvantages: Assumes a lossless line ($R=0$ and $G=0$), which is an approximation.; Frequency dependence is ignored in simple surge impedance calculations.

Applications: Power system protection against switching and lightning transients.; Designing surge arresters for transmission equipment.

Additional Info: The dimension of $\sqrt{L/C}$ is $[V/I] = \Omega$ (Ohms).. Option A ($ei = \sqrt{L/C}$) represents power-like dimensions, which is incorrect.. Option C and D involve the product of $L$ and $C$, which relates to velocity, not impedance.

Answer: B is correct — the ratio of the traveling voltage wave to the current wave is the surge impedance, defined as $\frac{e}{i} = \sqrt{\frac{L}{C}}$.

Exam Tip: Always remember that high capacitance (like in cables) lowers the surge impedance, leading to higher surge currents for the same voltage.

Examoogle · Answer

Option A: $ei = \sqrt{L/C}$

Examoogle · Answer

Option C: $ei = \sqrt{LC}$

Examoogle · Answer

Option D: $\frac{e}{i} = \sqrt{LC}$

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