This may be a stupid question but I'm missing something fundamental about energy conservation of electrical machines - I am sure I have forgotten something from basic machine theory but I haven't found out what thus far:
Let L, R, E be the equivalent model of a DC brushed motor winding (inductance, resistor, back-EMF).
Say we are braking the motor either by short-circuiting the windings, or applying the reverse voltage, let I be the current value. The mechanical power is -EI right? Energy conservation dictates this power is dissipated somewhere, and here it's RI^2.
Now, I close a switch and insert in series with the winding an additional braking resistor (for example when freewheeling the current goes back to the supply and into a braking resistor when the DC link regulator switch is closed). The braking power is still the same, -EI, since the current has not yet changed thanks to the inductor. However, now both the windings and the braking resistor dissipate more power than before the switch closed: (R+R2)I^2.
What am I missing? Is the inductor providing the power for the additional resistor - meaning the energy dissipated in the winding cannot be reduced for a given mechanical energy to be dissipated?
This is ultimately what I am trying to achieve, my winding cannot handle the mechanical energy I have to dissipate from the rotor when braking.