Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
For a given power delivered, if the working voltage of a distributor line is increased to n times, the cross-sectional area A of the distributor line, would be reduced to
n1тАЛA
n21тАЛA
2n21тАЛA
2n1тАЛA
n21тАЛA
Increasing the transmission voltage V reduces the required current I for a fixed power P=VI, which consequently reduces the power loss (I2R) and the volume of conductor material required ┬╖ If voltage is increased to n times, the cross-sectional area A is reduced to n21тАЛA to maintain the same percentage voltage drop and transmission efficiency.
Increasing the transmission voltage V reduces the required current I for a fixed power P=VI, which consequently reduces the power loss (I2R) and the volume of conductor material required ┬╖ If voltage is increased to n times, the cross-sectional area A is reduced to n21тАЛA to maintain the same percentage voltage drop and transmission efficiency.
P=VI тАФ Relationship between Power, Voltage, and Current
AтИЭV21тАЛ тАФ Relation between conductor cross-section and voltage for fixed power loss
The transmission line power loss is PlossтАЛ=I2R. Since P=VI, then I=VPтАЛ. Substituting this into the resistance formula R=╧БAlтАЛ, the power loss becomes proportional to V2AP2тАЛ. To keep power loss and percentage regulation constant while V increases by n, the area A must be reduced by n2.
Higher voltage transmission leads to significant savings in copper or aluminum conductor material.
The reduction in conductor cross-section follows an inverse square law with respect to the voltage increase factor n.
Increasing voltage is the most effective way to reduce capital expenditure on transmission line materials.
Reduced conductor material cost
Lower I2R power losses
Improved voltage regulation
Increased insulation costs
Higher tower clearance requirements
Complex switchgear and transformer insulation
High Voltage Direct Current (HVDC) transmission
Extra High Voltage (EHV) AC transmission systems
This relation holds strictly under the assumption of constant percentage voltage drop and constant power transmission.
Option A (1/nA) represents a linear reduction, which is incorrect as it does not account for the squared dependency of I2R losses.
B is correct тАФ By increasing the voltage by a factor of n, the conductor cross-sectional area required to maintain the same power loss reduces by a factor of n2.
Always remember that in power transmission calculations, voltage magnitude typically impacts parameters quadratically (V2) while current magnitude impacts losses quadratically (I2).