Ohms law works for linear loads (constant resistance or impedence) which your motor is not.
Better to think in terms of power P=E*I. The motor requires more power to overcome the resistance of the rails. Since E can't go up, I has to increase.
The intersting thing is that for a constant load, if you lower the voltage to a motor, the current goes up. That's the opposite of what you would expect from ohms law. But if you look at P=E*I, if P stays constant, and E goes down, I has to go up.
Edit: Someone will probably give me grief for not including power factor, since motors came into the discussion. But the basic relationships stay the same even if we start adding the difference between KVA and P.
Steve