What Determines The Amount Of "Current" In An Amp?

05-11-15: Mitch4t
.
300 wpc amp at 8 ohms plays 4 ohms at 450 wpc

300 wpc amp at 8 ohms plays 4 ohms at 600 wpc

Does one of the above amps necessarily have more current than the other? If an amp doubles with each halving of ohms, is that an indicator of its ability to deliver more current?

yes, the 300W/8Ohms, 600W/4Ohms amp has the ability to supply more current into the load when these 2 amps are compared side-side.
yes, when an amp can double in power for each halving of the load impedance is an indicator that such an amp can supply more current to the load compared to another amp does not double in power for each halving of the load impedance.

Is there an identifiable specification in an amp that will tell you how much current it will be able to deliver?

not really. Atmasphere/Ralph already addressed this point when he said that the industry does not have a standardized method the spec output current & what the manuf do is specify short-circuit current i.e. current delivery capability when the speaker binding posts are short-circuited for a short period of time (such as 10mS). It's no real measure of current since the music signal is faster moving than 10mS.
One hint that an amp can deliver high current to a speaker load is to see the power output specification - if the amp doubles in output power for each halving of the load impedance, it does indicate that such an amp has a large, high-current power transformer & a very robust output stage that can deliver high current. Amplifiers that come to mind are the older Krells, Gryphon Audio, Clayton Audio, Pass Labs, Threshold (to some extent 'cuz they didn't spec their amps below 4 Ohms most of the time).

The notorious Apogee Scintilla and Infinity Kappa 9 are two speakers that dip to amp-killing low ohms. What specification in and amp do you look for in its ability to drive a speaker like these. Is it current or wpc you would be looking for in a speaker like these?

I should be able to answer this one as I own a 1-ohm Apogee Scintilla. ;-) When selecting a suitable amp I looked for both WPC & current delivery capability. I found that looking at only one spec was not sufficient - I needed high current into a 1-Ohm impedance load & I needed voltage to prevent the output stage from slamming into the power rails.
For example: let's take your 300W/8 Ohm amp that you cited in your prev post. It needs a 50VAC secondary transformer to generate its 300W/ch. The manuf could install a 400VA/50VAC dual secondary power transformer. You can do the math - it means 8A of total secondary current. Since it's a stereo amp (I assumed this), it'll be 4A per channel total. That's not a lot of current when driving a Scintilla or a Kappa 9. Further the manuf could advertise that the output has 16 or 32 matched output transistors each rated for 1A. You might be impressed - what a mother load of output transistors; i'll get plenty of output power. Wrong! the current is limited by the 400VA/50VAC power transformer & it doesn't matter that the output stage has 16/32 match transistors. So, when you read the power output spec of such an amp, it'll be like your 1st cited amp: 300W/8, 450W/4 - it won't double in power as the load halves. For that to happen, the power transformer will have to be larger.

Also, how does current differ from watts per channel in the ability to drive a speaker?
.
Mitch4t

As you well know, Power = Voltage * Current.
For a high wattage amplifier to deliver high current into a load, the amp needs to have a large power transformer which is rated for high current. Otherwise, that high wattage amplifier has, what I call, 'empty watts' - it's a large number of watts without substantial current delivery support. It's a term coined by me for my personal use. And, as you can tell, 'substantial' is a very fuzzy term. How much is substantial? I do the calculation for each scenario that i'm evaluating & determine if it's substantial or not.

hope this helps....

Where can I purchase a Linear regulated power supply at a decent price?
For my Digital amplifier.? It would be greatly appreciated thank you,Paul.

Some speakers which dip to very low impedances at certain frequencies don't require lots of current, but rather an amp that is stable into a highly-reactive load that presents an almost dead-short operating condition, with, as Viridian mentioned, wild phase angles, a combination that make some amps oscillate in a state of instability. One such speaker is the original Quad, which was sometimes faulted for the sins of the amp driving it.

If you ain't got enough current, I can sell some Amperes for you (i can pour'em to the medicine bottle); trade-ins are OK as well.

05-11-15: Mitch4t
.
Thanks Viridian.

In the very big amps of old, they boasted large power supplies. Is it necessary for Class D amps to have a large power supply to deliver continuous high current into low ohms?

In general, yes, SMPS power supplies are capable of supplying large amounts of current into a low impedance. Today one can see several class-D amps capable of 20-30A into a low impedance such as 2 Ohms. Bill_k already cited the Merrill Veritas. There are a few others too - names are eluding me right now....
In a SMPS the amount of power delivered depends on the size of the power inductor & the size of the output power switches (that switch with PWM control, most often). Ultimately, in SMPS power supplies too the amount of output current is limited by the size of the AC power transformer because SMPS too have to take as input the AC from the wall outlet, rectify it to DC & regulate that for the class-D power amp. Whatever current the class-D power amp needs comes from the SMPS power supply & in turn the SMPS power supply takes its current from the wall outlet i.e. AC power transformer.
So, high current is possible thru a SMPS-based class-D power amp - just have to size the AC power transformer correctly (given that the SMPS design is correct for high current).
Many class-D amps are stated to be stable down to 2 Ohms but I see very few capable of stability into 1 Ohm. Part of the reason could be that very few 1 Ohm speakers exist today.