> I'm pulling about 20-30mA each preamp so it looks like a 10R will drop less than a volt .... What I don't know is how to calculate the wattage for the resistor.
0.030A times <1V is 0.030 Watts. You can hardly buy a resistor too small.
> What do I use as the current? The full 1A that the wart can supply?
Why not the 100+ Amps that the wart's cap (if extra-good) can supply (for a very short time)?
However there IS an issue. At the moment of contact the current is still HIGH. And the voltage is full no-load supply voltage. So big power. Power falls as the preamp cap charges, and the time is short.
Here's a plot. I assume your "12V 1A" supply really means 20% sag and >1A for some time will make smoke. So it is really a 14V supply with 2 Ohms of loss. This loss is mostly in the transformer, the cap is straight to the jack.
At the instant of connection, wart cap is at 14V and preamp cap is at zero V. Say there's NO resistance in the line or jack or caps. Current is then 14V/0r or INFINITE Amps (and Watts). A pair of real caps this size may be 1r total DCR. 14V/1r is 14 Amps, 14 Volts, 196 Watts.
Putting 10 Ohms in there makes 1.4 Amps, still 14V, 19.6 Watts. (Abbey is using the assumption that your wart CAN'T dump >1A, which would be valid for some switchers, but not a basic linear wart.) Time constant is like 10mS(?). In plot below, red spike is V(R68)*I(R68) or power in the 10 Ohm resistor. If checked at 1 Second it is 0.012W, no trouble. But AT plug-in it spikes to almost 20 Watts, and does not come down to 1W until 26mS.
Can a common 1/4W resistor stand this spike? Ratings are no help. They tend to say 200% for 1 Second, not milliSecond abuse.
Put 1W in a 1/4 resistor (12V in 150r 1/4W) while you are holding it. It gets HOT but it takes a second or more. (Discount, because it takes time for skin to heat-through to the nerve; this is just for concept.) If it takes OTOO a second to hot-up, how hot can it get in a few mS? Hot enough to burn the element?
The old-old Carbon Compositions had fat coal/clay elements and would stand all sorts of spike abuse for decades. Modern Film resistors obviously have less resistor-stuff and may burn-up faster. I would have no fear of using a 1/4W film part in this application for stage use. If I were protecting a military installation and the mission required constant hot-plugging, I might spec a fatter resistor (or even ramped power).