# Determining motor amps based on rpm and time

#### Chris Jones (cjonesy20)

Joined Jun 20, 2019
3
I'm taking a coursera/University of Colorado Boulder course on Motors and there's a question that none of the material covered and the instructors are MIA.

I'm not looking for a straight up answer, but some help in finding the right equations I would need to calculate this. "Final" current seems pretty straight forward at 5V/2ohm = 2.5 amps but I'm not sure how to use the 0.009 per rpm constant to figure out what it would be at t=20ms. Any help would be appreciated!

Suppose the motor resistance is 2 ohms, motor inductance is 5 milli-henries, external voltage is 5 volts, and the back EMF time constant is .009 per RPM.
As the motor accelerates, what is the motor current in milli-amps at time t = 20 milliseconds when the motor is running at 500 RPM. Ignore any oscillation of the back EMF voltage due to commutation. Type an integer value of milli-amps.

#### Chris Jones (cjonesy20)

Joined Jun 20, 2019
3
I took a stab at it and figured maybe 0.009 per rpm is voltage. So 500 rpm * 0.009 = 4.5V. So that means that 5V supply - 4.5V back emf = 0.5 V / 2 ohm = 0.25 amps. so 250 milli-amps. Why provide the 5 mH if it's not needed?

Joined Jul 18, 2013
19,730
The off off load current of a DC motor is virtually dependant on the inertia and friction (load) of the armature, as voltage increases, the supply-BEMF difference is fairly constant, so the current curve is fairly flat from 0 to max rpm.
This has been found by empirical testing using a 2.5hp 120v DC motor.
Max.

#### Chris Jones (cjonesy20)

Joined Jun 20, 2019
3
My experience with some worm-gear permanent magnet DC motors is that there's a huge spike in current at 0 rpm and then it tails off from there. Definitely not flat. I had to put supercapacitors in place to prevent overloading the power supply at startup (didn't want to put in any acceleration ramps).