As can be seen from the circuit diagram, the two resistors are connected in parallel, the voltmeter V measures the power supply voltage, the ammeter A 1 measures the R2 branch current, and the ammeter A measures the main current.

Because the voltage of the power supply is constant, when the slider is moved, the indication of voltmeter V remains unchanged, so A is wrong;

Because each branch in the parallel circuit works independently and does not affect each other, the current flowing through R 1 is unchanged when the slider moves;

When the slider of the sliding rheostat moves from the middle point to the right end, the resistance in the access circuit becomes larger. According to ohm's law, the branch current becomes smaller, that is, the indication of ammeter A 1 becomes smaller.

Because the main current in parallel circuit is equal to the sum of each branch current, the main current becomes smaller, that is, the indication of ammeter A becomes smaller, so C is wrong;

Because the ratio of voltmeter v to ammeter a is equal to the total resistance in the circuit, and the total resistance in the circuit increases gradually with the movement of the slider, the ratio of voltmeter v to ammeter a becomes larger, so c is wrong;

The difference between ammeter A and ammeter A 1 is equal to the current through R 1, but the current through R 1 is unchanged, so the difference between ammeter A and ammeter A 1 is unchanged, so D is correct.

So choose D.