Linear power supply

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I have built a 5 volt linear power supply to feed my computer, which consumes 3 amps@5vdc. I have used an LT 350 regulator with 2200uf filter capacitance & 1000uf as output capacitance. Everything is hard wired using a 16awg cable on the board. The load can't be kept close to the power supply so I have about 20 inches of the same wire that is connecting the power supply to the load. Is this OK or do I need to add a few small values of caps close to the load as well?
I have an Owon oscilloscope but have never learnt how to use it to check the ripple.
 
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Wirewound is not ideal as its self inductance negates the effect of the cap at higher frequencies.

A 0.5 watt part is fine. Although one end of the resistor or cap will be at 'ground' (and it doesn't matter which as they are in series) you should add the parts directly across the incoming feed to the PC.
 
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Like this:

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