Voltage equation for separately excited DC motor armature circuit

[theone]

Homework Statement

Homework Equations

The Attempt at a Solution

For the textbook diagram of a separately excited dc motor, the voltage equation for the armature circuit is given as

$V_t=E_a + I_aR_a$

But in the class notes, it says $V_t = V_a$
Firstly, I don't know if the $V_a$ refers to the induced armature voltage $E_a$ or the $I_aR_a$.

But either way, according to the voltage equation, shouldn't the two not be equal?

 

[vela]

From the hand-drawn diagram, it's pretty clear that $V_a = E_a + I_aR_a$.

 

[andrevdh]

The coils of the armature is represented by a pure inductor and a resistor in the equivalent circuit.
Going round the circuit we come to the conclusion that the supply voltage V_t is

V_t = E_a + I_a R_a

where E_a is the voltage over the pure inductor.
Next they introduce a "new" variable, the voltage drop over the armature as a whole V_a .
Clearly this has to be equal to the supply voltage V_t .