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ElectricalPower System

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For a transmission line with resistance (R), reactance (X) and negligible capacitance, the line constant A is

R + jX

R + X

Correct Answer

Concept & PrincipleElectricalPower System

Option A

Quick Summary: In a short transmission line where capacitance is neglected, the line is modeled as a simple series impedance $Z = R + jX$. The general ABCD constants represent the relationship between sending end and receiving end voltages and currents, where $A = 1 + ZY/2$; with shunt admittance $Y = 0$, the constant $A$ simplifies to unity.

💡 Explanation

In a short transmission line where capacitance is neglected, the line is modeled as a simple series impedance $Z = R + jX$ . The general ABCD constants represent the relationship between sending end and receiving end voltages and currents, where $A = 1 + ZY/2$ ; with shunt admittance $Y = 0$ , the constant $A$ simplifies to unity.

🔢 Key Formulas

$A = D = 1 + \frac{ZY}{2}$ — General ABCD constant definition

$Z = R + jX$ — Series impedance of the line

⚙️ Working Principle

The transmission line is represented by the Two-Port Network ABCD parameters. For a series impedance $Z = R + jX$ and shunt admittance $Y = 0$ , the transmission matrix is given by $T = [[1, Z], [0, 1]]$ . Since $A$ is the top-left element of this matrix, $A = 1$ .

📌 Key Points

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Short transmission lines are defined by lengths up to 80 km or voltages below 20 kV.
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For short lines, shunt capacitance is negligible ( $Y \approx 0$ ).
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In any reciprocal network, $AD - BC = 1$ ; for these lines, $A = D$ and $A = 1$ .
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The constant A is dimensionless.

✅ Advantages

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Simplifies power flow calculations for short distance lines.
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Reduces computational complexity of network matrices.

❌ Disadvantages / Limitations

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Not applicable for medium or long transmission lines where capacitance becomes significant.
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Ignores Ferranti effect which occurs due to line capacitance.

🛠️ Applications / Uses

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Distribution network modeling.
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Short-distance rural electrification analysis.

📄 Additional Information

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For short lines, $B = Z = R + jX$ , $C = 0$ , and $D = 1$ .
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Option C ( $R + jX$ ) represents the series impedance $B$ , not constant $A$ .

📊 Diagram / Illustration

✅

A is correct — For a short transmission line where shunt capacitance is negligible, the transmission constant A is equal to 1.

Core Concepts Used

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Two-Port Network Parameters Transmission Line Modeling ABCD Constants

💡 EXAM TIP

Always verify if the question asks for constant A, B, C, or D; remember that for short lines, A=D=1 and C=0.

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