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This is a general question where you will find no general answer.
Resolution...channel count.
Imagine a heating control for a house. A temperature sensor in a room. I expect the lowest useful temperature for the regulation is about 0°C, just to prevent water from freezing. The highest temperature maybe is 30°C.
So there is a useful range of 30°C...You want to adjust the room temperature in steps of 0.5°C. This gives 60 steps.
An ADC with a resolution of 6 bits (giving 64 steps) is enough.
There is no need for 10 bits resolution (0.03°C) or even more.
The same is with channels. In most rooms there is no need for multiple temperature sensors. One channel is enough.
Now imagine an audio signal. For good audio quality you need about 16 bits of resolution, 10 bits is maybe good enough for speech only, 6 bits is horrible.
And for audio equipment you will use at least two channels. So it makes sense to build 16 bit audio ADCs with two channels.
For coloured video you will need at least three channels.
For a three phase energy meter you may use three channels for voltage and another three channels for current.
More channels or less channels may not be usefull.
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If you need more information you should more precisely specify "channels": Most multi channel ADCs only have a MUX to select inputchannel. So only one signal can be converted in a time. But there are multi channel ADCs, that are able to convert multiple channels at the same time....
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An ADC is not only channel and resolution.
You could expand your question on:
Sample rate, noise, input voltage range, distortion, and many parameters more...
It is always a question on what the application needs.
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