In a DC motor, applied armature voltage drives current through the rotor winding. That current interacts with the magnetic field to produce torque, while rotation generates a back EMF that opposes the applied voltage.

Starting

At standstill,

$$\omega=0,$$

so the back EMF

$$E=k_e\Phi\omega$$

is initially zero. The armature current is then limited mainly by the armature resistance:

$$I_a\approx\frac{V}{R_a}.$$

Because $R_a$ is often small, starting current can be much larger than normal running current.

Acceleration and back EMF

Electromagnetic torque accelerates the rotor. As speed rises, back EMF rises and the current falls:

$$I_a=\frac{V-E}{R_a}.$$

The motor settles when electromagnetic torque balances the load and loss torques.

Load changes

If load torque increases, the rotor slows slightly. The lower speed reduces back EMF, which increases armature current and therefore electromagnetic torque until a new balance is reached.

Speed control

For approximately constant flux,

$$\omega\approx\frac{V-I_aR_a}{k_e\Phi}.$$

Changing armature voltage or magnetic excitation therefore changes operating speed, subject to current, commutation and magnetic limits.