Restricting movement of a DC motor ( replicating high load by holding it)
This question seems to have caused a lot of confusion because of the description of the power supply. As revised, we can assume that the power supply may be adequate for the test described.
The equivalent circuit for the motor is shown below. The back emf, e(t) is a voltage generated by the armature that opposes the current from the power supply. The emf is directly proportional to the rotational speed of the armature. If the motor shaft is prevented from turning, e(t) = 0. That means that the armature current is determined by the armature resistance Ra. Ra is quite small. Since the power dissipated in Ra is responsible for most of the losses in the motor its value is inversely proportional to motor efficiency. If the motor is switched on with rated voltage Va applied, the initial current may be on the order of ten times the rated motor current.
Since the current allowed by Ra can damage the motor very quickly, the blocked rotor test described in the question should only be performed using a supply voltage that is much less than the rated motor voltage, 10% for example. The objective of the blocked rotor test is to determine the values of Ra and La. Since the power supply output impedance can have an effect on the determination, the power supply used should have an output impedance that is mush lower than the motor impedance. The output voltage should be monitored to note any drop in voltage.
With the rotor blocked, when Va(t) is applied as a step increase from zero, the current is limited by Ra and La. The rise in voltage will follow an inverse exponential curve with the time constant RxL.
If the rotor is free to turn, the same limitation in current applies initially, but as the motor accelerates, the back emf will further limit the current. If the shaft is not connected to a load, acceleration will be determined by the motor torque, the inertia of the motor rotor, the bearing and brush friction and the aerodynamic drag of the air on the rotor. The effect on motor current will be a slightly slower rise in current, and a slightly lower peak current followed by the current decreasing to a value that represents the torque required to overcome the friction and drag.