Solution Electrical Numerical 10

Numerical 10: 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. 

Solution: Given Max voltage of each conductors = 200V

Phase angle between conductors = 20°

Conductors connected in series

Now, The Active part of EMF  $\displaystyle \mathrm{ = 200Cos0^o +200Cos20^o+200Cos40^o }$ = 541 V

The Reactive Part of EMF  $\displaystyle \mathrm{ = 200Sin0^o +200Sin20^o+200Sin40^o }$ = 197 V

$\displaystyle \mathrm{ Resultant\ EMF= \sqrt{541^2+197^2}\ = 575.75\, V }$ 

(i) RMS  of Effective Voltage = 0.707 x 575.75 = 407.055 V

(ii) Breadth Factor 

$\displaystyle \mathrm{K_{o}= \frac{Actual\ EMF\ Generated}{Total\ Possible\ EMF}\ =\ \frac{575.75}{3\times 200}\, = \, 0.959}$