Generated EMF - GATE EE Electrical Machines Free MCQ Test with solutions

Any of the above mentioned methods will produce EMF in the armature windings.

e = Nω_rΦsinω_rt-NdΦ/dtcosω_rt, for time invariant field flux dΦ/dt = 0 ⇒ e = Nω_rΦsinω_rt, is the general equation, and is applicable to both AC and DC systems.

f_r is called the rotational or speed frequency, since its value depends upon the relative velocity between the flux density wave and the armature coil.

e = E_maxcos(ω_rt-π/2)
ψ = NΦcosω_rt
It reveals that the speed or generated EMF lags by 90° the flux that generates it, and is true when flux is time invariant and is sine distributed in space.

The effect of short pitched coil is to reduce the generated EMF, and this reduction factor is cosε/2, and is referred to as coil pitch factor.

EMF induced = NΦω_rk_psinω_rt,
E_max = NΦω_rk_p when sinω_rt = 1
RMS value, E = E_max/√2 = √2πf_rk_pNΦ

The effect of short pitched coil is to reduce the generated EMF and this reduction factor is cosε/2 and is referred to as coil pitch factor.

In rotating electrical machines, the armature turns are usually distributed in slots rather than concentrated in single slot. This is essential from the view point of utilizing the armature periphery completely, and add mechanical strength.

E = √2πk_pk_df_rNΦ, k_d is the distribution factor.

A polyphase induction motor can be used as a frequency converter (or changer) for changing the supply frequency f to other frequencies sf and (2-s)f at the slip ring terminals.

The relative speed between rotor and rotating flux wave, i.e, (ω-ω_r) is referred to as the slip speed in rad/sec
slip speed = (ω-ω_r) rad/sec

Relative velocity between rotor winding and rotating flux wave becomes
(ω+ω_r) = ω+ω(1-s) = ω(2-s) and
E = 2πf(2-s)N_phrk_wΦ

For a P-pole machine, in n rev/sec, P/2n cycles/second are generated and cycles per second is referred to as frequency f of the EMF wave. Here in this question n=1
⇒ frequency per revolution = P/2
⇒ number of pole pairs.

N = 1200rpm,P = 6 and f = PN/120 = 60 cycles per sec.
1cycle = 360° electrical degrees = 2π electrical radians
f in electrical radians per sec = 60∗2π electrical radians/sec = 120π elect radians/sec
speed in mechanical radians/sec = 2/P(speed in electrical rad/sec) = 2/P(120π)=40π mechanical rad/sec.

 For the same value of peak flux density B_p, it is easy to see that average value of brush voltage could be more for a flat topped B-wave than for a sinusoidal flux density wave.