Correct Answer - Option 4 : decreased
Consider the transmission of electric power by a three-phase line
Let,
P = power transmitted in watts
V = line voltage in volts
cos φ = power factor of the load
The current (I) flowing through the system is given as,
\(I = \frac{P}{{\sqrt 3 \;V\;cos\phi }} \)
Resistance per conductor, \(R = \frac{{\rho l}}{a} \)
Total Power loss (W) is given as,
\(W = 3{I^2}R = 3{\left( {\frac{P}{{\sqrt 3 \;V\;cos\phi }}} \right)^2} \times \frac{{\rho l}}{a} = \left( {\frac{{{P^2}\rho l}}{{\;{V^2}{{\cos }^2}\;\phi \;a}}} \right) \)
\(W\propto \frac{1}{{{V^2}}} \)
Where,
l = length of the line in meters
R = resistance per conductor in ohms
ρ = resistivity of conductor material
a = area of X-section of conductor
The load current is given as,
From the above equation, we can say that if voltage increased then line loss will decrease and vice versa.
