current versus watts

Is high current as important to quality dynamic sound as high watts.

You can't separate the two as current and power are proportional.

current = square root of (power divided by ohms)

300 watts into 8 ohms takes about 6.12 amps of current

600 watts into 4 ohms takes about 12.24 amps of current

Some amps can handle delivering the current needed for 8 ohms at full power but run out before they can deliver the current needed for full power into 4 ohms.

The better way to say it is that the amp has to be able to deliver enough current to develop the requested power, not which one is more important.

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Amps aren't rated for "max current" since that depends on the load. Most amps are voltage amplifiers; they try to hold the output voltage at a certain level for a given input and the amount of current they produce depends on the load. The 300W/8ohm amp above produces a maximum of 49V. This 49V divided by 8 ohms is 6.12 amps (Ohms law.) If the load drops to 4 ohms then it will still try to maintain the 49V so it needs to deliver 12.24A. If loaded with 2 ohms it will try to deliver 24.48A, try to deliver 49 amps into 1 ohm, and so forth. At some point any amp will be unable to deliver the required current.

All else being equal an amp that can deliver more current is preferable over one that can't, but things are never equal. Some speakers have big dips in their impedance at certain frequencies and theoretically benefit from a high current amp, or better stated benefit from an amp that can deliver high amounts of current when required to do so. So yes, this headroom is a desirable characteristic if the speakers you are using call for it but is not the sole criteria for picking an amplifier.

If you google Ohms law and speaker impedance and you can find a wealth of material about these fundamental concepts.

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