A duplex lap$-$wound armature has $128$ coils with $20$ turns per coil. Assume that this armature is rotated with wind power between eight poles at a speed of S revolutions per second. The flux per pole is $0\mathrm{.}05$ Wb$.$ Each conductor has a resistance of $0\mathrm{.}008$ ohm. Answer the following questions:

a$)$ Find the rotor speed at revolutions per minute.

b$)$ Calculate the number of parallel current paths in the armature.

c$)$ Calculate the total number of conductors on the armature.

d$)$ What is the induced voltage at armature terminals at no load?

e$)$ Calculate the armature$$resistance$.$