How does a change in input series capacitance would affect the probe compensation?

How does a change in input series capacitance would affect the probe compensation. What really happens when a capacitance of probe is adjusted for compensation?

probe compensation

Probe? If you mean oscilloscope probe, this is the explanation (from https://en.wikipedia.org/wiki/Test_probe):

Passive scope probes

A passive 10x probe. Notice the switch in the probe handle that allows to choose between 1x or 10x attenuation. Passive scope probes contain no active electronic parts, such as transistors, so they require no external power.

The most common design inserts a 9 megaohm resistor in series with the probe tip. The signal is then transmitted from the probe head to the oscilloscope over a special coaxial cable that is designed to minimize capacitance and ringing. The resistor serves to minimize the loading that the cable capacitance would impose on the DUT. In series with the normal 1 megohm input impedance of the oscilloscope, the 9 megohm resistor creates a 10x voltage divider so such probes are normally known as either low cap(acitance) probes or 10X probes.

Because the oscilloscope input has some parasitic capacitance in parallel with the 1 megohm resistance, the 9 megohm resistor must also be bypassed by a capacitor to prevent it from forming a severe RC low-pass filter with the 'scope's parasitic capacitance. The amount of bypass capacitance (capacitor tuning screw) must be carefully matched with the input capacitance of the oscilloscope so that the capacitors also form a 10x voltage divider. In this way, the probe provides a uniform 10x attenuation from DC (with the attenuation provided by the resistors) to very high AC frequencies (with the attenuation provided by the capacitors).

10x probes cable capacitance

"Because the oscilloscope input has some parasitic capacitance in parallel with the 1 megohm resistance, the 9 megohm resistor must also be bypassed by a capacitor to prevent it from forming a severe RC low-pass filter with the 'scope's parasitic capacitance"
How does the addition of a capacitor in parallel to 9M ohm resistor prevents the formation of severe low pass filter?

oscilloscope 10x probe compensation

Detailed explanations and analysis can be found here:

**broken link removed**