Question
Download Solution PDFThe volume of copper required for an AC transmission line is:
I. proportional to the voltage
II. proportional to power factor
III. inversely proportional voltage and proportion to current
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Let, P = Transmitted power
V = Line voltage in volts
cosϕ = Power factor
l = Length of the line
R = Resistance
ρ = Resistivity
A = Cross-sectional area
Consider the transmission of electric power by a three-phase line.
\(P= { \sqrt{3}VIcosϕ}\)
\(I= { P\over \sqrt{3}Vcosϕ}\)
The total power loss is given by:
\(W = 3I^2R\)
\(W = 3({ P\over \sqrt{3}Vcosϕ})^2({\rho l\over A})\)
\(A= ({ P\over Vcosϕ})^2({\rho l\over W})\)
Volume \((Vol) = A \times l\)
\(Vol= ({ P\over Vcosϕ})^2({\rho l^2\over W})\)
Therefore, the volume of copper required for an AC transmission line is inversely proportional to voltage and proportion to the current.
Last updated on Jul 1, 2025
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