Shaft speed–
Armature current–
Back EMF–
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The simple motor equations

Torque is proportional to current: T = k x I. Back EMF is proportional to speed: E = k x speed. The supply must cover both the back EMF and the resistance loss, so V = E + I x R, which gives speed = (V minus I x R) / k.

This teaching model uses a small hobby motor with k = 0.02 volt seconds per radian, an armature resistance of 1 ohm and 0.1 amp of friction current. The spin in the scene is slowed down about fifty times so you can follow it.

Try it: set the load to zero and slide the voltage from 3 to 24 volts. Speed rises almost in step with voltage while current barely changes. Then hold the voltage and raise the load, and watch speed fall as current climbs.

Why stalled motors get hot

If the shaft is held still there is no back EMF at all, so current is limited only by the winding resistance. That stall current can be many times the running current, which is why a jammed motor overheats quickly.

Sources

How to cite this model

Avid Solutions International. (2026, November 11). How a brushed DC motor turns [Interactive 3D model]. Avid Field Lab. https://avidsolutionsintl.com/explore/dc-motor

Last updated November 11, 2026

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