# Back emf in motors and capacitors

1-this is what is written in my book:
E= Ir+E' where E' is the back emf, r and E' are constants
P(mechanical)=E'*I
an electrical motor functions only if the generator connected across its terminals delivers a positive potential difference that exceeds its back emf.
So my question is, why are they regarding the back emf as constant quantity that characterizes each motor though the current across the motor is not always constant?

2-"in case we connected a pure inductor(coil) to AC generator, during a part of the cycle, energy is actually transferred from the inductor (load) back into the voltage source. we get a net power dissipation of zero."
how could energy be transferred to a generator??
in this case, a current is traversing the circuit without dissipating energy, will the current traversing the coil in this situation has a very large intensity as the case of a short circuit?????

3-is there any proof why the average power equals cosine the phase angle (Φ) between voltage and current(case of sinusoidal voltage)???

4-does the back emf in motors have sinusoidal form???

5-P(mechanical)=E'*I where E' is the back emf
is this formula of mechanical power converted by the motor right??

6-does the electrical energy converted to mechanical energy by the motor increase when the motor is loaded? will the intensity of the traversing current increase?

7-in case a motor is loaded, will the mechanical power converted by the motor be smaller although the intensity of current has increased??
since P(mechanical)=E'*I where E' is the back emf, E' decreases when the motor is loaded???

8-what causes Inrush current drawn by an electrical device when first turned on in case we are supplying the device AC current?

9-why does the capacitor gets the same voltage of the generator after it is disconnected?

10-i have understood how a capacitor stores charge, but my question is how does capacitor stores energy? is storing charge the same as storing energy?