Problem 103-14    Source:  Problem prepared by the website author.

A DC electric motor, in the independent configuration, operates with a constant field current and is rotating at 1,400 rpm. Powered with a voltage of 200 V the armature current is 12 A. When we reduce the load on the motor shaft, maintaining the same supply voltage, the armature current became 7 A. Assume that the motor has an armature resistance of 0.12 Ω. Determine:

a) the new engine speed;

b) the power developed by the motor when I_A = 12 A;

c) the power developed by the motor when I_A = 7 A;

d) the torque developed by the engine in both cases.

Solution of the Problem 103-14   

Item a   

To solve this problem we must find the voltages induced when I_A is equal to 12 A and 7 A. Then:

So, let's calculate the new machine speed using eq. 103-21 after some algebraic work.

Carrying out the calculation, we get:

Item b   

The power for I_A = 12 A is:

Item c   

The power for I_A = 7 A is:

Item d   

To calculate the torque we will calculate the angular velocities in both cases using the eq. 103-12. Like this:

Therefore, the torques, using the eq. 103-18, are: