The 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

  1. Only II
  2. Both I and II
  3. Only III
  4. Only I
  5. Both I and III

Answer (Detailed Solution Below)

Option 3 : Only III
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Detailed Solution

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Concept:

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.

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