An alternator is to deliver 5.0 kW of electrical power at a terminal voltage of 250 V (rms) to a purely resistive load. The alternator employs a coil of N turns, each turn being a rectangle 20 cm × 15 cm, and operates in a radial magnetic field of uniform magnitude. The maximum allowable rms current in the coil circuit is 25 A. The rotor will be driven at a steady 3000 revolutions per minute.
(a) Calculate the peak value of emf that must be generated per phase to obtain the given terminal voltage.
(b) Derive an expression relating the magnetic field magnitude B, the number of turns N and the rotor speed to the peak emf and hence determine the minimum product BN required to meet the specification.
(c) If the design constraint fixes the magnetic field at 0.40 T, find the least integer value of N that satisfies the requirement.
(d) Using the value of N obtained, compute the rms current in the load and verify that it does not exceed the specified limit.