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When it comes to simple circuit analysis, there is millions of tutorials on how to analyze a resistor circuit, a RC circuit, or those involving LED the non-ohmic devices. However, I did not find a simple and clear tutorial on how DC motors behave within a circuit. I did some experiment, and only got more confused over the result. A brushless motor rated for 0.4A 5V when connected to a 9V it runs full speed without a problem, but then I add a little resistor to limit some current suddenly the motor hardly turns at all.

Summary of question: what is the behaviour of DC motors in a circuit? What does the rating 5V 0.4A mean? (the voltage drop? the forward voltage? etc.)

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If it's a "brushless motor" that's running off of 9V DC, then it's a motor and a controller -- and all bets are off, because the controller could be anything.

The 5V 0.4A rating means that if you put 5V on it and load it to it's specified torque it'll pull no more than 0.4A (or if it's a brushless fan, it'll just pull around 0.4A).

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Summary of question: what is the behavior of DC motors in a circuit? What does the rating 5V 0.4A mean? (the voltage drop? the forward voltage? etc.)

DC motors are difficult to model because the power and current that the motor uses is dependent on the speed and torque load of the motor.

The way to tell is to see if there is a datasheet for the motor and look at torque vs speed curves if it is a DC motor.

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