## DC Machine

**
Shunt
Generator
For a shunt generator with armature induced voltage E_{a}, armature
current I_{a} and armature resistance R_{a}, the terminal
voltage V is:
V = E_{a} - I_{a}R_{a}
The field current I_{ f} for a field resistance R_{ f} is:
I_{ f} = V / R_{ f} **

The armature induced voltage E_{a}
and torque T with magnetic flux
F
at angular speed
w are:

E_{a} = k_{ f}Fw
= k_{m}w

T = k_{ f}FI_{a}
= k_{m}I_{a}

where k_{ f} and k_{m} 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 P _{e} for a
shunt generator is:
P_{e} =
wT
= E_{a}I_{a} = k_{m}w
I_{a}
**

**
Shunt Motor
For a shunt motor with armature induced voltage E _{a}, armature
current I_{a} and armature resistance R_{a}, the terminal
voltage V is:
V = E_{a} + I_{a}R_{a}
The field current I_{ f} for a field resistance R_{ f} is:
I_{ f} = V / R_{ f} **

The armature induced voltage E_{a}
and torque T with magnetic flux
F
at angular speed
w are:

E_{a} = k_{ f}Fw
= k_{m}w

T = k_{ f}FI_{a}
= k_{m}I_{a}

where k_{ f} and k_{m} 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 P _{e} for a
shunt motor is:
P_{e} =
wT
= E_{a}I_{a} = k_{m}w
I_{a}
**

Series Motor

For a series motor with armature induced voltage E_{a}, armature
current I_{a}, armature resistance R_{a} and field
resistance R_{ f}, the terminal voltage V is:

V = E_{a} + I_{a}R_{a} + I_{a}R_{ f}
= E_{a} + I_{a}(R_{a} + R_{ f})

The field current is equal to the armature current.

The armature induced voltage E_{a}
and torque T with magnetic flux
F
at angular speed
w are:

E_{a} = k_{ f}Fw
I_{a} = k_{m}w
I_{a}

T = k_{ f}FI_{a}^{2}
= k_{m}I_{a}^{2}

where k_{ f} and k_{m} 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 P _{e} for a
series motor is:
P_{e} =
wT
= E_{a}I_{a} = k_{m}w I_{a}^{2}
**