Problem 102-2    Source:   Adapted from Example 7-4 - page 448 - CHAPMAN, Sthephen J. -    Book: Fundamentals of Electric Machines - 5th Edition - Ed. McGraw-Hill - 2013.

A DC generator of 12 poles has a simplex wave-winding armature containing 144 coils of 10 turns each. The electrical resistance of each turn is 0.011 Ω. Its flux per pole is 0.05 Wb and it is rotating at a speed of 200 rpm.

a) How many current paths are there in this machine?

b) What is the induced voltage E_A?

c) What is the effective armature resistance of this machine?

Solution of the Problem 102-2   

Item a   

The number of current paths in this machine is given by eq. 102-10, repeated below.

So, replacing the variables by their respective values, remembering that the armature is simplex, so m = 1, we find

Item b   

To calculate the induced voltage in the armature it is necessary to calculate the number of conductors in the machine, Z, given by eq. 102-04 shown below.

Then, replacing the variables by their respective values, we find

We are now in a position to calculate the constant K_a using eq. 102-13, shown below.

Then, replacing the variables by their respective values, we find

Item c   

The rotor of this machine is traversed by two parallel paths, each consisting of Z/2 = 1 440 conductors. As a loop is formed by two conductors (one that leaves the commutator, crosses the rotor through a slot and returns through another slot closing a loop), then the total turns equals the number of conductors divided by two, or 720 turns. Therefore, the resistance of each current path is

Since the rotor has two parallel paths, the effective armature resistance is