Your best bet is method C:
Use your solar panels with an MPPT charging circuit and an output voltage the same as the existing AC charger. Use that to charge the existing lithium battery.
That's the safest, surest, most efficient way to use solar panels to power your bike.
You'll probably have to let it charge for several hours in the sun. Bigger panels ...
A transistor does nothing on its own. However, that is not strictly a transistor. It's an IC with a power transistor and other stuff in it.
Also motors do not drive current, they draw current. But I would say that no matter what you do 1.5A is far too undersized for a motor that can draw up to 20A. And such a motor would not be able to do very much running ...
The power supply voltage dropping 2-3 volts when the motor load increases means that the power supply cannot deliver all the current that the motor would take. You should consider a power supply with a greater output capacity so that its output stays at 12V for the full range of loads that you expect to put on the motor.
Some power supplies may very well ...
The voltage and current rating of a motor, relay, solenoid, etc. is based on a variety of factors:
wire gauge used for each winding
insulation on windings and connectors
materials used in construction
allowed temperature increase (which is related to chosen materials)
duty cycle (energize-time versus off-time)
expected lifetime and abuse (used in an office ...
The iron in the field magnet structure will retain some magnetism even without any current in the winding so the field and hence the back-emf will not drop to zero. The actual remaining amount depends upon the specifics of the material and the magnetic structure. Dynamos rely upon this remanence to bootstrap operation at start-up.
I want to drive the car on house with a decent speed. Not like that
For similar performance to the stock setup you want a similar voltage. AA cells put out about 1.5v to 1.1V each depending on load and discharge state, so to replace a 6 cell AA battery you want something that delivers from 6.6V to 9V. It also needs enough capacity to run ...
DC motor speed control does not normally use series, shunt compound or any other connection of the field to the same supply as the armature. The controller provides a separate regulated power supply for the field. The field current is maintained at a constant value unless field weakening is used to extend the operating speed above the normal base speed of ...