Amin has a magnetic levitation toy, the principle of which is to use electromagnets to generate magnetic force, so that magnetic dolls can float stably, and its structure is shown in the figure.

A. As can be seen from the meaning of the question, the doll floats stably, and the lower end is the S pole, so the upper end of the coil is the S pole. According to the right-hand spiral law, the power supply is DC, the terminal B is the positive pole of the power supply, and the terminal A is the negative pole of the power supply, so A is wrong and B is right;

C, if the number of turns of the coil around the soft iron increases, thus increasing the magnetic field of the coil and leading to the increase of the maximum floating height of the doll, then c is correct;

D. If the resistance value of the variable resistor increases, the current in the coil decreases, resulting in a decrease in the maximum floating height of the doll, so d is wrong;

So: BC.