Two identical coils are fixed on the same shaft at right angles to each other and rotate together in a uniform magnetic field. Each coil produces an emf whose maximum value is 120V. The shaft rotates at constant angular speed, and the emfs from the two coils are 90∘ out of phase with each other.
a. (i) Show that, at any instant, the magnitude of the vector sum of the two emfs is given by ε=ε12+ε22, where ε1 and ε2 are the instantaneous emfs in the individual coils.
b. (ii) Hence determine the rms value of the resultant emf produced by the pair of coils.
c. (iii) If this two-phase supply feeds a purely resistive load that draws 10A rms, calculate the average power delivered to the load.