ElectricalPower System

If the receiving-end voltage and current are numerically equal to the corresponding sending-end values, that is, |Vs| = |Vr| and |Is| = |Ir|, then such a line is called

An infinite line

A natural line

A tuned line

A loss-less line

Correct Answer

Concept & PrincipleElectricalPower System

Option A

An infinite line

Quick Summary: An infinite line is a theoretical transmission line where the receiving-end voltage and current magnitudes are identical to the sending-end values because the line is terminated by its characteristic impedance. In this condition, the input impedance of the line equals its characteristic impedance ($Z_{in} = Z_0$), resulting in no reflections.

💡 Explanation

An infinite line is a theoretical transmission line where the receiving-end voltage and current magnitudes are identical to the sending-end values because the line is terminated by its characteristic impedance. In this condition, the input impedance of the line equals its characteristic impedance ( $Z_{in} = Z_0$ ), resulting in no reflections.

🔢 Key Formulas

$Z_{in} = Z_0 \frac{Z_R + Z_0 \tanh(\gamma l)}{Z_0 + Z_R \tanh(\gamma l)}$ — General input impedance formula

$Z_{in} = Z_0$ — Condition for an infinite line where $Z_R = Z_0$

⚙️ Working Principle

When a transmission line is terminated with a load impedance equal to its characteristic impedance ( $Z_R = Z_0$ ), all incident power is absorbed by the load. Consequently, the voltage and current profiles are uniform throughout the line, behaving as if the line were infinitely long without any reflected waves returning to the source.

📌 Key Points

▸
Input impedance is independent of line length $l$ .
▸
Reflection coefficient $\Gamma = 0$ at the load.
▸
Uniform voltage and current magnitude along the line.
▸
The line appears as a pure resistance $Z_0$ to the source.

✅ Advantages

▸
No reflected waves exist on the line.
▸
Maximum power transfer condition is inherently satisfied.

❌ Disadvantages / Limitations

▸
Theoretical construct; physically infinite lines do not exist.
▸
Practical limitations due to line losses ( $\\alpha \\neq 0$ ) making perfect impedance matching difficult.

🛠️ Applications / Uses

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Foundation for analyzing wave propagation in transmission lines.
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Impedance matching techniques in high-frequency RF systems.

📄 Additional Information

▸
A 'natural line' (Option B) usually refers to a line operating at surge impedance loading (SIL).
▸
A 'tuned line' (Option C) refers to a line with length $\\lambda/2$ or $\\lambda/4$ where input impedance equals load impedance or its inverse.
▸
A 'loss-less line' (Option D) has $R=0$ and $G=0$ but does not necessarily imply $V_s = V_r$ .

📊 Diagram / Illustration

✅

A is correct — An infinite line is defined by the condition where the line is terminated by its characteristic impedance, resulting in no reflection and identical magnitudes at both ends.

Core Concepts Used

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Characteristic Impedance Reflection Coefficient Transmission Line Equations

💡 EXAM TIP

Always remember that for an infinite line, the input impedance is purely equal to the characteristic impedance $Z_0$ , regardless of the electrical length of the line.

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