Please show all work An elementary two-pole three-phase 50 Hz alternator has a r

Question

Please show all work

An elementary two-pole three-phase 50 Hz alternator has a rotating flux of 0.0516 Wb. The number of turns in each phase coils is 20. Its shaft speed is 3000 rpm and its stator winding factor is 0.96. Determine the speed of the rotor in rad/sec. Determine the magnitude of the peak per phase voltage. Determine the three-phase voltages as function of time. The rms phase voltage of the generator if the stator windings are connected in delta. The rms terminal voltage if the stator windings are connected in wye. Determine the value of the K constant of the generator if the angular velocity is in electrical radians per second. Determine the value of the K constant of the generator if the angular velocity is in mechanical radians per second. Determine the new three-phase voltage values of the internal generated voltage. Determine the three-phase voltages as function of time.

Explanation / Answer

a) the speed in rps can be obtained by dividing rpm with 60 so speed in rps equal to3000/60=50

b) I rms per phase voltage is obtained from emf equation

=4. 44*kw*f*T*phi

So as per given data phi=. 0516wb

f=50hz,T=20,Kw=.96

Peak Emf per phase=220v*root(2)=312v

ii)as each phase have a phase difference of 120degrees so the each phase votages

Va=312sinwt,

Vb=312sin(wt-120)

Vc=312sin(wt-240)

C)rms voltage of stator if connected in delta

In delta phase voltage is equal to line voltage so rms voltage equal to what the voltage we obtained in (b) =220v

D)rms terminal voltage is the line voltage for wye Connected line voltage equal to root (3)times so answer is root (3)*220=381v

Thank u

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