Final answer:
The angular speed of the rotor in an alternator is 188.5 rad/s. The three-phase voltages are sinusoidal functions of time. The rms phase voltage for delta-connected windings and the rms terminal voltage for wye-connected windings depend on the maximum induced voltage; precise values need specific figures for calculation.
Step-by-step explanation:
To solve the presented questions regarding the alternator, we apply the principles of electromagnetic induction and AC electricity.
(a) The Angular Speed of the Rotor
The angular speed ω can be found by converting the shaft speed from rev/min to rad/s:
ω = 1800 rev/min × (2π rad/rev) × (1 min/60 s) = 188.5 rad/s.
(b) Three Phase Voltages as a Function of Time
The induced electromotive force (emf) in each phase coil can be determined using Faraday's law of induction, which relates the rate of change of the magnetic flux through a coil to the induced emf:
E(t) = N × dΦ/dt × winding factor,
where E(t) is the instantaneous voltage, N is the number of turns, and dΦ/dt is the rate of change of flux.
Since the alternator is generating a three-phase voltage, each phase will yield a sinusoidal function of time:
E(t) = Emax × sin(ωt + ϕ),
where Emax is the maximum voltage, ω is the angular frequency, t is time, and ϕ is the phase offset for each phase.
(c) RMS Phase Voltage for Delta-Connected Windings
For delta-connected windings, the rms phase voltage Vrms is equal to the peak voltage Emax divided by √2:
Vrms = Emax/√2.
(d) RMS Terminal Voltage for Wye-Connected Windings
For wye-connected windings, the rms terminal voltage VL is √3 times the phase voltage:
VL = √3 × Vrms.
However, to provide specific numerical answers, we need the exact values for the peak flux, frequency, and the other variables involved.