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

$-1.0$

Zero

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option B

$-1.0$

Quick Summary:

The voltage reflection coefficient ( $\Gamma_V$ ) at a load is defined by the ratio of the reflected voltage wave to the incident voltage wave. For a short-circuited line, the load impedance ( $Z_L$ ) is zero, resulting in a reflection coefficient of $-1.0$ .

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\Gamma_V = \frac{Z_L - Z_0}{Z_L + Z_0}$ — General voltage reflection coefficient

$\Gamma_V = -1$ — Reflection coefficient at a short-circuited termination ( $Z_L = 0$ )

⚙️ Working Principle

When an incident wave traveling along a transmission line with characteristic impedance $Z_0$ encounters a load $Z_L$ , a portion of the wave is reflected. The coefficient is calculated as $\Gamma_V = \frac{Z_L - Z_0}{Z_L + Z_0}$ . In the case of a short circuit ( $Z_L = 0$ ), the formula simplifies to $\Gamma_V = \frac{0 - Z_0}{0 + Z_0} = -1$ , meaning the reflected wave is equal in magnitude but opposite in polarity to the incident wave, effectively canceling the voltage at the shorted end.

📌 Key Points

▸
A short-circuited termination forces the total voltage at that point to be zero.
▸
The negative sign indicates a 180-degree phase shift for the reflected voltage wave.
▸
For an open circuit ( $Z_L = \infty$ ), the reflection coefficient is $+1.0$ .
▸
For a matched line ( $Z_L = Z_0$ ), the reflection coefficient is $0$ .

✅ Advantages

▸
Helps in understanding transient voltage surges in power systems.
▸
Essential for analyzing standing waves on transmission lines.

❌ Disadvantages / Limitations

▸
Reflection at discontinuities causes over-voltages that can stress insulation.
▸
Requires impedance matching to prevent signal degradation in communication systems.

🛠️ Applications / Uses

▸
Protection coordination in high-voltage transmission lines.
▸
Reflectometry (TDR) for detecting faults in power cables.

📄 Additional Information

▸
A short circuit represents a discontinuity in the transmission line where the characteristic impedance is mismatched.
▸
Option A (1) is the reflection coefficient for an open-circuited line.
▸
Option C (Zero) is the reflection coefficient for a matched load ( $Z_L = Z_0$ ).

📊 Diagram / Illustration

✅

B is correct — The reflection coefficient for a short-circuited line is $-1.0$ because the load impedance is $0$ , resulting in total negative reflection of the incident voltage wave.

Core Concepts Used

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Transmission Line Transients Reflection Coefficient Impedance Mismatch

💡 EXAM TIP

Remember: Short circuit results in $\Gamma_V = -1$ (phase reversal) and $\Gamma_I = +1$ (current doubling), while open circuit results in $\Gamma_V = +1$ and $\Gamma_I = -1$ .

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