Resistence value in the solenoid coil

What you're referring to is called "back EMF," which appears to raise the resistance of the motor winding by opposing the flow of current.

When a DC motor is operated as a generator with no electrical load (and therefore no IR losses in the armature), the voltage generated at a particular speed is pretty much a linear function. e. g. The motor/generator produces 1 volt @ 100 rpm, 2 volts @ 200 rpm, and so on.

When operated as a motor with a mechanical load, in order to maintain a desired speed, a certain amount of current must pass through the armature to produce the torque necessary to run the load at that speed (power is consumed). Part of the power used is to overcome the losses in the armature winding resistance, e. g. I²R.

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No, the direct current of the DC motor will not increase to infinite values. For the right answer we have to imagine the equivalent circuit of DC motor. There is the back emf against the suppling voltage with resistance between them. This resistance is nearby equal to the coil resistance, but may be higher if there is serious non-compensated armature reaction. So, the motor current is equal to voltage difference divided to this resistance. When any of resistive force doesn't applied to the motor, its rotation velocity will arise to the value that will produce back emf is equal to supplying voltage. So, the voltage difference will be zero together with the motor current. When the supplying voltage changes its polarity immediately, the difference between supplying voltage and back emf will arise very seriously (at the moment minus of back emf will have the same sign as the voltage) and it causes to huge motor current. This current has first to neutralize all kinetic energy of motor rotor and then to insert the same kinetic energy but in the opposite direction of motor rotation. This current will slow down to zero when rotation velocity will arise to steady-state value.

Simply put

The resistance value of 2 ohm is a function of the length and composition of the coil and will not change.

The total load is the 2 ohm in parallel with the back emf.

I = E/(2 ohm + Back emf )

The current will increase due to the work being done to overcome the back EMF.

Ohms law: current is inversly proportional to resistance

Therefore to get increased current either the voltage has to increase or the total apparent resistance has to decrease.