Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option A

Quick Summary:

The reflection coefficient ( $\Gamma$ ) of a transmission line represents the ratio of the reflected voltage wave to the incident voltage wave at the load. For an open-circuited transmission line, the load impedance ( $Z_L$ ) is infinite, resulting in a reflection coefficient of 1, meaning the reflected wave is equal in magnitude and phase to the incident wave.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

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

$\Gamma = 1$ — Reflection coefficient for open circuit ( $Z_L = \infty$ )

⚙️ Working Principle

The reflection coefficient is defined as $\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$ , where $Z_L$ is the load impedance and $Z_0$ is the characteristic impedance of the line. As the line is open-circuited, $Z_L \to \infty$ . Taking the limit as $Z_L \to \infty$ , we find $\Gamma = \lim_{Z_L \to \infty} \frac{1 - Z_0/Z_L}{1 + Z_0/Z_L} = \frac{1-0}{1+0} = 1$ . This implies total reflection occurs at the open end without phase reversal.

📌 Key Points

▸
An open-circuited line acts as a perfect reflector.
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The incident voltage and reflected voltage add up to twice the incident voltage at the open end.
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Total reflection occurs, meaning no power is dissipated at the load terminal.

✅ Advantages

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Voltage doubling occurs at the open end, useful in high-voltage testing.
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Useful for calculating standing wave patterns in lines.

❌ Disadvantages / Limitations

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Can lead to high voltage stress and potential insulation failure.
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Causes standing waves which increase transmission losses.

🛠️ Applications / Uses

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Pulse-echo testing for fault location.
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Impedance measurement techniques (e.g., slotted line).

📄 Additional Information

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When the line is short-circuited ( $Z_L = 0$ ), $\Gamma = -1$ .
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When the line is matched ( $Z_L = Z_0$ ), $\Gamma = 0$ (no reflection).
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Option D is incorrect as the coefficient is bounded by -1 and 1 for passive loads.

📊 Diagram / Illustration

✅

A is correct — The reflection coefficient for an open-circuited transmission line is 1 because the load impedance is infinite.

Core Concepts Used

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Transmission Line Theory Reflection Coefficient Impedance Matching

💡 EXAM TIP

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

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