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V: voltage between the wires in 2 wire case I and between the outer and the neutral in 3 - wire case II

P: Power transmitted R1: Resistance per unit length for case I. R2: Resistance per unit length of outer wires in case II

Resistance of the neutral = 2 R 2 per unit length I in 2- wire case = P/V Power loss = 2 I 2 R = 2 (P/V) 2 R1 I in 3- wire case, and assume equal loads ,i.e I1 = I2, I through N=0

I = P / (2V) Power loss = 2 ( P /2V)2 R2 For equal power loss : 2 / (P/V )2 R1 = 2 ( P/2V)2 R2 R2 = 4 R1 Cross section of the outer is of that in the 2- wire Copper ratio: 3 wire = (2 x ) + (1/2 x ) = 5 = 31.25 2 wire 2 x 1 16

Reduction in case of using 3 wire = 68.75 %

If the neutral has the some cross section as the outer, the ratio is : 3 wire = (2 x ) + (1 x ) = 3 = 37.5 % 2 wire 2 x 1 8

Reduction in case of using 3 wire = 62.5 %

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Let E voltage between conductors in d-c. , I is current Power = E I Loss = 2 R2 I R : resistance of each wire per unit length for DC system

For star connected 3 phase, maximum voltage E, r.m.s value = E / 2 I is the r.m.s. value of the line current Power = 3/ 2 E I cos Loss = 3 R I2 R : resistance per wire for 3 phase system

For same transmitted power: E I = 3/ 2 E I cos

And same power loss: 2 R I2 = 3 R I2

Hence R = R / ( 3 cos2 )

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Voltage Drop (Approximate)

Power Loss Amount of conductor

Type of AC system

1.0 1.0 1.0 2- wire 0.25 0.25 1.5 3-wire

Single Phase

0.5 0.5 1.5 3-wre 0.25 0.25 2 4-wire 0.25 0.25 2.5 5-wire

Two Phase

0.167 0.167 1.5 3-wire * Three Phase

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0.5 0.5 1.5 3-wire ** 0.167 0.167 2 4-wire 0.042 0.042 3 6-wire 0.042 0.042 3.5 7-wire

Six Phase

* Star voltage same as single phase ** Delta voltage same as single phase

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