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The reflection coefficient of a short-circuited line for voltage is

– 1

0.5

Zero

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option A

– 1

Quick Summary:

The reflection coefficient for voltage on a transmission line is defined as the ratio of the reflected voltage wave to the incident voltage wave at the load termination. For a short-circuited line, the load impedance is zero, leading to a complete reversal of the incident voltage wave upon reflection.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\Gamma_v = \frac{Z_L - Z_0}{Z_L + Z_0}$ — General expression for voltage reflection coefficient

$\Gamma_v = -1$ — Specifically for short-circuit conditions ( $Z_L = 0$ )

⚙️ Working Principle

The reflection coefficient ( $\Gamma_v$ ) is given by $\Gamma_v = \frac{Z_L - Z_0}{Z_L + Z_0}$ , where $Z_L$ is the load impedance and $Z_0$ is the characteristic impedance of the line. For a short circuit, $Z_L = 0$ . Substituting this into the formula results in $\Gamma_v = \frac{0 - Z_0}{0 + Z_0} = -1$ . This negative sign indicates that the reflected voltage wave is equal in magnitude but opposite in polarity to the incident wave, forcing the total voltage at the shorted end to be zero.

📌 Key Points

▸
A reflection coefficient of $-1$ indicates total reflection with a 180-degree phase shift.
▸
For an open-circuited line ( $Z_L = \infty$ ), the reflection coefficient is $+1$ .
▸
For a matched line ( $Z_L = Z_0$ ), the reflection coefficient is $0$ .
▸
The total voltage at the short-circuited terminal is $V_{incident} + V_{reflected} = V + (-V) = 0$ .

✅ Advantages

▸
Allows for simplified boundary condition analysis in power system transients
▸
Helps in predicting wave behavior at line discontinuities

🛠️ Applications / Uses

▸
Fault analysis in power systems
▸
Transmission line transient modeling
▸
Time Domain Reflectometry (TDR) measurements

📄 Additional Information

▸
Short circuit represents a perfect voltage sink where potential difference must be zero.
▸
Option B (1) is the reflection coefficient for an open-circuited line.
▸
Option D (Zero) is the reflection coefficient for a perfectly matched line.

📊 Diagram / Illustration

✅

A is correct — The reflection coefficient for voltage is -1 because the short circuit forces the total voltage at the termination to be zero by canceling the incident wave with an equal and opposite reflected wave.

Core Concepts Used

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Transmission Line Theory Wave Propagation Boundary Conditions Reflection Coefficient

💡 EXAM TIP

Always remember that for a short circuit, voltage is zero ( $\Gamma_v = -1$ ) and for an open circuit, current is zero ( $\Gamma_i = -1$ , while $\Gamma_v = +1$ ).

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