An alternator is to be designed so that the total length of copper wire used in the armature windings does not exceed 450m. Each turn forms a rectangle of mean perimeter 0.60m. The machine must deliver 240V rms at 50Hz while rotating at 120r.p.m.. The maximum magnetic flux density in the air gap is 0.22T and each turn encloses an area of 200cm2.
(a) Express the rms emf in terms of the number of turns N and the given machine parameters.
(b) Using the wire-length constraint, write an inequality for N and hence find the feasible range of N.
(c) Within this range, determine the smallest N that still meets the output specification.
(d) Evaluate whether the design goal is achievable under the given constraints, and justify your conclusion with numerical values.