How does a computer's processing capacity affect the amount of ram you can use?

All programs and data are executed from memory (RAM)

but it first needs to be fetched from wherever it is stored.If there is insufficient free memory, then some memory must be freed up by writing t to disk in the paging file. You can minimize the chances of this happening by maximizing the amount of memory in the PC.

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The second impact is memory speed, especially the speed at which data can be transferred between RAM and the CPU. Data is actually transferred to cache memory on the CPU chip from main memory before it is executed,and then results are written back to main memory. The speed of this data transfer is affected by the design of the system, and the speed and quality of RAM installed, and by the setup of RAM timing in BiOS.