Can I use this resistor in a crossover?

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Yes you can use it ... it might be a bit 'overkill' but that is never a bad thing :)

5,6 ohm and 6,2 ohm are also very close values (6,2 ohm is closest), so without knowing what speakers you are building, I would say that you should not be able to detect any big differences in th sound
 
Resistors are the place to cheap out on XO builds- sandcast/cement are fine. The slight inductance is rarely an issue unless you're doing significant very high frequency shaping, and even a few non-inductive sandcasts (paralleled to right value, and several for power handling) are very cheap relative to a decent coil.
 
RH0256R000FE02 | Vishay RH Series Axial High Power Wire Wound Resistor 6Ω 1% 25W 50ppm/C | Vishay

Is this resistor usable in a crossover? it seems to be the only findable 6 ohm resistor. Building a pair of overnight sensations... or would it be ok to swap for a 5.6 or a 6.2
If the 5.6 or 6.2 are lower priced, you can use the 5.6 in series with an 0.4 ohm, or the 6.2 in parallel with a 1/(1/6-1/6.2)=186 ohms. Do the second, a 180 ohm resistor will be cheaper and more available than a less-than-1 ohm resistor, and either only needs to be rated at 1/2 or 1/4 watt or so.

I found the schematic here:

https://f48a8583-a-62cb3a1a-s-sites...EkZP21n3mB7jN1AQ8fSlDA-Xx8gw==&attredirects=0

If you want to be uh, "precise," you can measure the outputs of the tweeters, and change the 6 and 10 ohm resistors to make the outputs equal. I don't know offhand if different drivers of the same model vary in sensitivity enough to worry about, but if so, there you are.

Going from 6 to 5.6 or 6.2 would change the tweeter level by about (taking a SWAG) a tenth of a dB, which is pretty much an inaudible change.
 
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