Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option D

180°

Quick Summary:

The reflection coefficient ( $\Gamma$ ) at the load end is defined by the ratio of the reflected voltage wave to the incident voltage wave. For a short-circuited load, the load impedance is $Z_L = 0$ , which results in a reflection coefficient of $-1$ , corresponding to a phase shift of $180°$ .

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$ — General formula for reflection coefficient

$\Gamma_{sc} = -1$ — Reflection coefficient for short-circuited line

⚙️ Working Principle

When a traveling wave reaches a short circuit, the boundary condition requires the total voltage at the load to be zero. To satisfy this, the reflected wave must be equal in magnitude but opposite in polarity to the incident wave ( $V_r = -V_i$ ). This $180°$ phase inversion ensures that the incident and reflected waves cancel each other out at the point of short circuit.

📌 Key Points

▸
Short circuit implies $Z_L = 0$ .
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Reflection coefficient $\Gamma = -1$ signifies a phase change of $180°$ .
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The incident and reflected waves interfere destructively at the load.
▸
Voltage at the short circuit terminal is always zero.

✅ Advantages

▸
Enables determination of fault location in power lines.
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Allows analysis of surge propagation characteristics.

❌ Disadvantages / Limitations

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Results in total reflection, preventing power delivery to the load.
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Can cause high-voltage transients if the line is not properly terminated.

🛠️ Applications / Uses

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Power system protection (Fault location).
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Time Domain Reflectometry (TDR) for cable testing.

📄 Additional Information

▸
For an open-circuited line ( $Z_L = \infty$ ), $\Gamma = +1$ , which corresponds to $0°$ phase shift.
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Option A (Zero) is incorrect as it represents a perfectly matched line ( $Z_L = Z_0$ ).

📊 Diagram / Illustration

✅

D is correct — The reflection coefficient for a short-circuited line is $-1$ , which represents a phase reversal of $180°$ .

Core Concepts Used

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Traveling wave theory Boundary conditions in transmission lines Reflection coefficient

💡 EXAM TIP

Always remember: Short circuit ( $Z_L=0$ ) gives $\Gamma=-1$ ( $180°$ ), Open circuit ( $Z_L=\infty$ ) gives $\Gamma=+1$ ( $0°$ ), and Matched line ( $Z_L=Z_0$ ) gives $\Gamma=0$ .

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