A long overhead transmission line is terminated by its characteristic impedance. Under this operating conditio

Question

A long overhead transmission line is terminated by its characteristic impedance. Under this operating condition, the ratio of the voltage to the current at different points along the line will

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Option D: Remain the same at all points

Explanation & Concepts:
When a transmission line is terminated by its characteristic impedance $Z_0$, the line is said to be 'matched'. Under this condition, there is no reflected wave, and the ratio of voltage to current is constant at every point along the line, equal to $Z_0$.

Working Principle: The voltage and current at any point $x$ on a lossy transmission line are given by $V(x) = V^+ e^{-\gamma x} + V^- e^{\gamma x}$ and $I(x) = \frac{V^+}{Z_0} e^{-\gamma x} - \frac{V^-}{Z_0} e^{\gamma x}$. If the line is terminated by $Z_L = Z_0$, the reflection coefficient $\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$ becomes zero, meaning $V^- = 0$. Consequently, the ratio $\frac{V(x)}{I(x)} = Z_0$ remains constant regardless of the position $x$.

Key Formulas: $Z_0 = \sqrt{\frac{R + j\omega L}{G + j\omega C}}$ — characteristic impedance of a transmission line; $\frac{V(x)}{I(x)} = Z_0$ — constant ratio when terminated by $Z_0$

Key Points: Matched termination prevents reflections on the line.; A matched line behaves as if it were infinitely long.; The input impedance of a matched line is independent of the line length.; Maximum power transfer occurs when source impedance equals characteristic impedance.

Advantages: Elimination of standing waves; Prevention of signal reflection/distortion

Disadvantages: Not always possible due to varying load conditions; Requires impedance matching networks for non-ideal loads

Applications: RF transmission lines; Telecommunication cabling; Pulse power systems

Additional Info: If $Z_L 
eq Z_0$, standing waves are formed, and the ratio $V/I$ varies as a function of the distance from the load.. Option D is the correct physical interpretation of a matched transmission line.

Answer: D is correct — Because the line is terminated by its characteristic impedance, no reflection occurs, ensuring the voltage-to-current ratio remains constant at $Z_0$ throughout the line length.

Exam Tip: Always remember that a line terminated in $Z_0$ is 'electrically invisible' to the source; it simply looks like a fixed resistor $Z_0$ regardless of the line length.

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Option A: Progressively increase from the sending-end to the receiving-end

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Option B: Progressively increase from the receiving-end to the sending-end

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Option C: Remain the same at the two ends, but is higher between the two end being maximum at the centre of the line

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