# Armature and terminal voltages in DC machines

In the below page I am trying to grasp the way the terminal voltage and armature voltage are related to each other.

## Below is my attempt to understand their relation:

Do you agree with my interpretation?

The source:

FE Reference Handbook 10.0.1

ISBN 978-1-947801-11-0

• The graph at the top of your inserted diagram is for an AC motor yet, the question is about DC motors. – Andy aka Jan 21 at 14:42
• @Andy aka , I just copied the whole page. I mean by chance it came to be on the same page. I thought this way it's more respectful to the author!!! – OMAR Jan 22 at 7:12

Firstly, the graph at the top of your inserted diagram is for an AC motor yet, the question is about DC motors. I assume that was an oversight.

I just copied the whole page. I mean by chance it came to be on the same page. I thought this way it's more respectful to the author!!!

No, I don't think so; it just led to confusion. You can respect the author by providing proper attribution as you have partially done at the base of your question.

Do you agree with my interpretation?

There is an error and it's how you have represented $$\V_a\$$ in the DC motor - it is in series like this: -

The error you made is assuming that $$\V_a\$$ is in parallel with the armature inductance $$\L_a\$$. The back emf in that inductor must always be shown to be in series with the inductor.

And, for the generator it is exactly the same; all three components are in series. This also means that when unloaded, $$\V_a\$$ exactly equals the output voltage $$\V_T\$$. When loaded then $$\V_a\$$ is going to be bigger than $$\V_T\$$.

The torque-speed characteristic of an induction motor appears to have nothing to do with the rest of the question.

The diagram showing the relationship of terminal voltage and armature voltage is correct for the equivalent circuit as shown. However in a physical motor, the resistance is distributed from one end of the winding to the other and armature voltage is the same as terminal voltage. Rather than showing the inductance and resistance separately, most representations show the armature winding in series with an ideal voltage source that represents the generation of a back EMF in a motor or the generated voltage in a generator.

• I just copied the whole page. – OMAR Jan 22 at 7:10