A. When the sliding contact of the sliding rheostat slides upward, the resistance of the sliding rheostat becomes larger, the total resistance of the circuit becomes larger, and the total current remains unchanged, so the terminal voltage of this circuit becomes larger, while the total current remains unchanged, so the voltage of the parallel part becomes larger, while the fixed resistance of the parallel part remains unchanged, so the current flowing through the fixed resistance becomes larger, so the current flowing through the ammeter becomes smaller, so A is wrong and B is correct;

C. According to the characteristics of series-parallel circuit, it is known that the ratio of the reading change value of voltmeter to that of ammeter is equal to a constant resistance, so the ratio of the reading change value of voltmeter to that of ammeter remains unchanged, so C is correct and D is wrong.

So choose BC