40.MET March 2019 Q.8(B)

Three conductors fitted side by side in the stator of a salient-pole alternator. Each generates maximum voltage of 200V (sinusoidal). The angle subtended at the centre of the stator between adjacent conductors is 20 electrical degrees. If the three conductors are connected in series, find
(i) the r.m.s. value of the effective voltage and
(ii) the ‘breadth factor’ Using the theory that is the basis of this problem, give one reason why three-phase current has been introduced.

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Given

E1 = E2 = E3 =200V
Angle 1 = angle 2 = angle 3 = 20 deg
Max possible EMF = 600 (CONNECTED IN SERIES )

To find

i) Rms value
ii) Breadth factor

Solution

Resolving the phasor into horizontal and vertical components

Horizontal component = E1 Cos 0 + E2 cos 20 + E3 Cos 40
                                     = 200 cos 0 + 200 cos 20 + 200 cos 40
                                     = 541.14 V

Vertical component  = E1 sin 0 + E2 sin 20 + E3 sin 40
                                 = 200 sin 0 + 200 sin 20 + 200 sin 40
                                 = 196.96 V

Resultant EMF = Square root of (541.142 + 196.962)
                               = 576 V

i) RMS value = 0.707 x Max EMF
                      = 0.707 x 576
                      =  407.23 V
ii) Breadth factor = Resultant EMF / Max possible EMF
                             = 576 / (200+200+200)
                             = 0.96