stability

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1) Depends on how unstable the amp is. If it's very unstable then it will be obvious, with the output oscillating at a particular frequency, usually causing heating of the output devices. If it's marginally stable then you may see bursts of oscillation. An oscilloscope is indispensable here.

A good test is to put a square wave into the amp and look for ringing at the output. If there is no ringing then the amp should be perfectly stable. A lot of ringing and you have a problem. You may want to test for stability with a capacitive load too.

2) For stability of course. BTW, you mean R + C at the output. If there's an L then it's not part of the Zobel network, although still there for stability.

3) It provides a low impedance path to ground at high frequencies. This helps compensate for the rising output impedance of the amp at high frequencies and/or inductive loads.
 
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