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Equivalent GMD of Transposed Line

For a transposed 3-phase transmission line, the mutual distances between the conductors are 4 m, 4 m, and 5 m, respectively. What is the equivalent mutual Geometric Mean Distance (GMD) of the line?
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Answer & Explanation
Correct AnswerD. ∛80 m

Quick Explanation

For a transposed 3-phase line, equivalent mutual GMD is the cube root of the product of the three mutual spacings. Thus Dm = ∛(4×4×5) = ∛80 m.

Formula / Key Relation

Dm = ∛(Dab Dbc Dca) = ∛(4×4×5) = ∛80 m
Equivalent GMD of Transposed Line explanatory diagram

Detailed Explanation

Correct Answer

D — ∛80 m

Explanation

For a transposed 3-phase line, equivalent mutual GMD is the cube root of the product of the three mutual spacings. Thus Dm = ∛(4×4×5) = ∛80 m.

Key Concept

Equivalent GMD of Transposed Line

Formula

Dm = ∛(Dab Dbc Dca) = ∛(4×4×5) = ∛80 m

Exam Point

Three mutual distances → multiply all three, then take cube root.

Common Mistake

Do not take a square root; a 3-phase transposed line uses the cube root of three spacings.

Quick Trick

Three mutual distances → multiply all three, then take cube root.

Common Mistake

Do not take a square root; a 3-phase transposed line uses the cube root of three spacings.

Exam Tip

Three mutual distances → multiply all three, then take cube root.

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