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GATE 2022 EE – Question 14

Power Systems · Basic concepts of electrical power generation, AC and DC transmission concepts, Models and performance of transmission lines and cables · 1 mark · Multiple choice

The geometric mean radius of a conductor, having four equal strands with each strand of radius 'r', as shown in the figure below, is

Diagram for GATE 2022 EE question 14
  1. $4r$
  2. $1.414\,r$
  3. $2r$
  4. $1.723\,r$

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Correct answer: (D) $1.723\,r$

Explanation

The four touching strands sit at the corners of a square of side $2r$ (diagonal $2.828r$). The self GMR of each strand is $r'=0.7788r$. The GMR is the 16th root of the product of all $4\times4$ distances: $\text{GMR}=\left[(0.7788r\cdot2r\cdot2r\cdot2.828r)^4\right]^{1/16}=(8.81r^4)^{1/4}=1.723r$.