An overhead line with surge impedance of 400 Ω is terminated t... | Electrical MCQ | Examoogle

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An overhead line with surge impedance of 400 Ω is terminated through a resistance R. A surge traveling over the line will not suffer any reflection at the junction, if the value of R is

$100 \ \Omega$

$200 \ \Omega$

$400 \ \Omega$

$800 \ \Omega$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option C

$400 \ \Omega$

Quick Summary:

A surge traveling on an overhead line encounters no reflection when the terminating resistance is equal to the surge impedance of the transmission line. This condition ensures perfect impedance matching, allowing the entire surge energy to be absorbed by the resistor without any portion being reflected back towards the source.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\rho = \frac{R - Z_c}{R + Z_c}$ — Reflection coefficient at a resistive termination

$V_{reflected} = \rho \cdot V_{incident}$ — Magnitude of the reflected wave

⚙️ Working Principle

When a traveling wave reaches a junction with impedance $Z_2$ , the reflection coefficient is defined as $\rho = \frac{Z_2 - Z_1}{Z_1 + Z_2}$ . For no reflection to occur, the reflection coefficient $\rho$ must be zero. Setting $\frac{R - Z_c}{Z_c + R} = 0$ leads to $R = Z_c$ , where $Z_c$ is the surge impedance of the line.

📌 Key Points

▸
Reflection coefficient $\rho$ is zero when $R = Z_c$ .
▸
Surge impedance $Z_c$ for an overhead line is typically between 400 to 500 Ω.
▸
If $R > Z_c$ , the reflected voltage is positive.
▸
If $R < Z_c$ , the reflected voltage is negative.

✅ Advantages

▸
Eliminates standing waves on the transmission line
▸
Prevents voltage build-up due to wave reflection
▸
Ensures maximum power transfer to the termination load

❌ Disadvantages / Limitations

▸
Requires high-precision resistors matching the line surge impedance
▸
Thermal dissipation capacity of the resistor must be high for surges

🛠️ Applications / Uses

▸
Termination of long transmission lines
▸
Surge protection circuits
▸
High-frequency communication signal transmission

📄 Additional Information

▸
For an open circuit, $R = \infty$ , $\rho = 1$ (full reflection with same polarity).
▸
For a short circuit, $R = 0$ , $\rho = -1$ (full reflection with opposite polarity).

📊 Diagram / Illustration

✅

C is correct — A surge experiences no reflection if the termination resistance equals the surge impedance of the line ( $R = 400 \ \Omega$ ).

Core Concepts Used

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Surge Impedance Reflection Coefficient Impedance Matching

💡 EXAM TIP

Always remember that for any discontinuity, if the load impedance matches the surge impedance, the line behaves as if it is infinitely long, absorbing all incoming wave energy.

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