# Dc motor clarification?

1. May 25, 2015

### theone

1. The problem statement, all variables and given/known data

2. Relevant equations

3. 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?

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2. May 25, 2015

### vela

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

3. May 26, 2015

### 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 Vt is

Vt = Ea + Ia Ra

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