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Home » AC Fundamentals » Prove that Volume of The conductor is Inversely proportional to the squire of Voltage ( Vol = 1/V2). And what is the effect of this relation on Transmission and Distribution System.

# Prove that Volume of The conductor is Inversely proportional to the squire of Voltage ( Vol = 1/V2). And what is the effect of this relation on Transmission and Distribution System.

Prove that Volume of The conductor is Inversely proportional to the squire of Voltage ( Vol = 1/V2). And what is the effect of this relation on Transmission and Distribution System.

Power in Three Phase Circuits    P = 3 V I Cosθ   OR     I = P / √3 V Cos θ            (1)
Law’s of resistance =                 R = ρ (l /A)                                                               (2)
Power Loss in Three Phase Circuits = P = 3 I2R                                                         (3)
Putting the Values of I and R from Equation (1) and (2) into Equation (3).
P = 3 (P / √3 V Cos θ)2 x [ρ (l/A)]
P = 3 (P2/3 V2 Cos2 θ) x ρ (l /A)
P = W = P2 ρ l / V Cos2 θ A… OR … A = P2 ρ l / V2 Cos2θ W                            (4)
Volume of the conductor in Three Phase System= Vol = 3A x Length                           (5)
Putting the value of “A” from Equation (4) into Equation (5)
Vol = 3 P2 ρ l / W V2 Cos2θ
Hence Proved that Volume of the Conductor is inversely proportional to the squire of Voltage
Volume of the Conductor = Vol 1/V2

Effect of this relation ( Vol = 1/V2)  on Transmission and Distribution System (i.e. Power System)
Actually, this relation has a very important rule in Transmission and Distribution System (i.e. in Power System)

As we proved that Volume of the conductor s inversely proportional to the squire of voltage, it meant that if we increase the level of voltage for transmission and distribution purpose, then volume of the conductor (in other words, Size of the Conductor) will reduce twice.

This is also a part of the answer of the question that why we transmit power at high voltage (when voltage increased then current decreased because generated power is constant)

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