Power rating of 12v dc motor can be few watt to kw depend upon design and size e.g. tap recrder cd motor and industrial carriages ,lifter and automobiles etc.etc. Also powerful supply sources are required for big 12 v motors and battery cell for small.
Because power = 12v * current. This current changes with load and maximum current that can pass safely through the motor - depends on the coil wire thickness and heat dissipation mechanism.
So if you try to stop the shaft spinning while supplying voltage, the current will increase proportional to coil resistance (motor is a practical short-circuit in this case) and it will consume high current that might damage the voltage source and the motor itself.
“The torque created by DC motor directly relies on the number of charges (electrons usually) passing in the conductor and how fast they are conducted. Interestingly, you can create high current using large stream of electrons (big river) moving slowly or small stream (small river) of electrons moving fastly.” For large stream you need thicker wire as lot of electrons can flow slowly, creating less viscosity/frictional loss.
But don't jump to a conclusion that 12v/4.5 = 2.66A. when motor rotates, it will create opposite emf, so current is reduced to a point where the speed of rotation will create enough opposite emf (equal & opposite to applied emf.) and this opposite emf depends on speed of rotation (assuming magnetic flux is constant i.e. u don't swap the magnets u use while comparing). Thats why it will try to maintain the speed, at a given voltage assuming your voltage source can give any current and motor can withstand any current. But you know what happens in reality. Either your source or motor will fry after giving a particular max torque in motor due to high current .
The coil resistance will dissipate more heat at high current, reason for frying your motor.
Assuming you have a ideal independent volt source,
If you can dissipate heat from within the coil like ‘frozen' queen, then power rating of motor will increase
If the coil wire is thicker, the power rating will increase.
If the coil insulation is good and you try to increase the voltage, increases the speed hence power rating increases.
