Question

The e.m.f generated in an alternator is independent of :

1. Speed
2. Type of alternator
3. Series turns per phase
4. Coil span

Answer 1

Correct Answer - Option 2 : Type of alternator

EMF Equation of Alternator:

The emf induced by the alternator or synchronous generator is three-phase alternating in nature. Let us derive the mathematical equation of emf induced in the alternator.

Let,

Z = number of conductors in series per phase.

Z = 2T, where T is the number of coils or turns per phase. One turn has two coil sides or a conductor as shown in the below diagram.

P = Number of poles.

f = frequency of induced emf in Hertz

Φ = flux per pole in webers

 K_p= pitch factor, K_d = distribution factor

N = Speed of the rotor in rpm (revolutions per minute)

N/60 = Speed of the rotor in revolutions per second.

Time is taken by the rotor to complete one revolution,

dt = 1/(N/60)= 60/N second

In one revolution of the rotor, the total flux ϕ cut by each conductor in the stator poles,

\({\bf{d}}ϕ = ϕ {\bf{P}}\;{\bf{weber}}\)

By faraday’s law of electromagnetic induction, the emf induced is proportional to rate of change of flux.

Average emf induced per conductor = \(\frac{{{\bf{d}}ϕ }}{{{\bf{dt}}}} = \frac{{ϕ {\bf{P}}}}{{\frac{{60}}{{\bf{N}}}}} = \frac{{ϕ {\bf{NP}}}}{{60}}\)

We know, the frequency of induced emf

\({\bf{f}} = \frac{{{\bf{PN}}}}{{120}}\;,\;{\bf{N}} = \frac{{120{\bf{f}}}}{{\bf{P}}}\)

Submitting the value of N in the induced emf equation, We get

Average emf induced per conductor = \(\frac{{ϕ {\bf{P}}}}{{60}} \times \frac{{120{\bf{f}}}}{{\bf{P}}} = 2ϕ {\bf{f}}\;{\bf{volts}}\)

If there are Z conductors in series per phase,

Average emf induced per conductor = \(2ϕ {\bf{fZ}} = 4ϕ {\bf{fT}}\;{\bf{volts}}\)

RMS value of emf per phase = Form factor x Average value of induced emf = 1.11 x 4 Φ f T

RMS value of emf per phase = 4.44 Φ f T volts

The obtained above equation is the actual value of the induced emf for full pitched coil or concentrated coil. However, the voltage equation gets modified because of the winding factors.

Actual induced emf per phase (E) = 4.44 K_p K_d Φ f T volts

Conclusion: Hence EMF induced in the transformer is independent of the type of Alternator used.