The voltage equation of a DC motor describes the relationship between the applied voltage, the motor's back electromotive force (EMF), the current flowing through the motor, and the motor's characteristics. In a DC motor, the voltage equation is commonly known as the "DC motor equation" or "motor equation."
The voltage equation of a DC motor is given by:
=
+
⋅
V=E+I⋅R
a
Where:
V is the applied voltage to the motor terminals.
E is the back EMF generated by the motor, which opposes the change in current and is proportional to the motor's rotational speed (angular velocity).
I is the current flowing through the motor.
R
a
is the armature resistance of the motor.
This equation highlights the balance between the applied voltage, which pushes current through the motor, and the back EMF, which opposes the flow of current due to the motor's rotation. The armature resistance,
R
a
, represents the internal resistance of the motor's armature winding.
The back EMF (
E) is calculated using the formula:
=
⋅
E=K⋅ω
Where:
K is the motor's back EMF constant (also known as the voltage constant or speed constant), which is determined by the motor's design and characteristics.
ω is the angular velocity of the motor in radians per second.
In practical applications, the voltage equation is crucial for understanding the relationship between the applied voltage, the motor's speed, and the current drawn. It's used for designing and controlling DC motor systems, such as adjusting the speed or torque of the motor by varying the applied voltage.