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I have been reading around about back EMF and their derivations for simple DC motors. However for some reason, the step between obtaining the total emf of the motor from summing the individual emf of the coils is not very clear. For example:

Induced emf due to single coil: [itex]e = d∅_c/dt[/itex]

Since the flux linking a coil is: [itex]∅_c = ∅ Sinωt[/itex]

Therefore the induced emf is: [itex] e = ω∅ Cosωt [/itex]

Since there are several coils all around the rotor, each one has a different emf due to its position (i.e each one has a different flux change through it). Therefore, total emf is the sum of the individual emfs.

This means, [itex]E_b = K ∅ ω_m [/itex] <<< How?

First of all, I don't understand how the [itex]Cosωt[/itex] disappears to obtain the final expression. Secondly, what parameters define the constant K? In some place I read, [itex] K = 2 N/\pi [/itex], while in other places it stated [itex] K = 2 N R B L [/itex]. Why is it different for each case and how is it derived in the above proof?

The above derivation is from end of page 5/start of page 6 of the following source: http://vlab.ee.nus.edu.sg/~bmchen/courses/EG1108_DCmotors.pdf.

Warm Regards,

Oz

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# How to Derive constant of total back/counter EMF for DC motors?

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