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An alternator on open-circuit generates 360 V at 60 Hz when the field current is 3.6 A. Neglecting saturation, determine the open-circuit EMF when the frequency is 40 Hz and the field current is 2.4 A.
1. 110 V
2. 140 V
3. 210 V
4. 160 V

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Correct Answer - Option 4 : 160 V

Concept :

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

Kp = pitch factor, Kd = distribution factor

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

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

Time taken by the rotor to complete one revolution

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

Single turn coil

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

dϕ = ϕP weber

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

Average emf induced per conductor = (dϕ / dt) = (ϕNP / 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 = \(\frac{{\phi {\bf{P}}}}{{60}} \times \frac{{120{\bf{f}}}}{{\bf{P}}} = 2\phi {\bf{f}}\;{\bf{volts}}\)

If there are Z conductors in series per phase,

Average emf induced per conductor = 2ϕfZ = 4ϕfT 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 = 4.44KpKdΦfT volts

From above equation we come to know that

Emf ϕ f

E1/E2  = (ϕ1f1) / (ϕ2f2)

If saturation is neglected then ϕ ∝ If

E1 / E2 = (If1f1) / (If2f2)

Calculations :

Given E1 = 360 V, If1 = 3.6 A, f1 = 60 Hz

If2 = 2.4 A, f2 = 40 Hz

∴ E2 = (E1If2f2) / (If1f1)

= (360 × 40 × 2.4) / (3.6 × 60)

= 160 V

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