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DC Machine

 

Shunt Generator
For a shunt generator with armature induced voltage Ea, armature current Ia and armature resistance Ra, the terminal voltage V is:
V = Ea - IaRa
The field current I f for a field resistance R f is:
I f = V / R f

The armature induced voltage Ea and torque T with magnetic flux F at angular speed w are:
Ea = k f
Fw = kmw
T = k f
FIa = kmIa
where k f and km are design coefficients of the machine.

Note that for a shunt generator:
- induced voltage is proportional to speed,
- torque is proportional to armature current.

The airgap power Pe for a shunt generator is:
Pe =
wT = EaIa = kmw Ia

Shunt Motor
For a shunt motor with armature induced voltage Ea, armature current Ia and armature resistance Ra, the terminal voltage V is:
V = Ea + IaRa
The field current I f for a field resistance R f is:
I f = V / R f

The armature induced voltage Ea and torque T with magnetic flux F at angular speed w are:
Ea = k f
Fw = kmw
T = k f
FIa = kmIa
where k f and km are design coefficients of the machine.

Note that for a shunt motor:
- induced voltage is proportional to speed,
- torque is proportional to armature current.

The airgap power Pe for a shunt motor is:
Pe =
wT = EaIa = kmw Ia

Series Motor
For a series motor with armature induced voltage Ea, armature current Ia, armature resistance Ra and field resistance R f, the terminal voltage V is:
V = Ea + IaRa + IaR f = Ea + Ia(Ra + R f)
The field current is equal to the armature current.

The armature induced voltage Ea and torque T with magnetic flux F at angular speed w are:
Ea = k f
Fw Ia = kmw Ia
T = k fFIa2 = kmIa2
where k f and km are design coefficients of the machine.

Note that for a series motor:
- induced voltage is proportional to both speed and armature current,
- torque is proportional to the square of armature current,
- armature current is inversely proportional to speed for a constant induced voltage.

The airgap power Pe for a series motor is:
Pe =
wT = EaIa = kmw Ia2