It is on the lower passenger side of the firewall.
it takes a group 75. a good battery would be an ac delco 75-60.
If you mean filter/dryer it is up front attached to the condenser. If you are looking for a cabin filter, It does not have one.
The engine computer controls the fuel and ignition systems, along with the ac compressor, alternator, and cruise control. The transmission computer controls the transmission. The abs computer does abs brakes. The airbag computer controls the airbag. Etc.
Look under the hood in the power distribution box and you will see a group of relays and it will be the top one on row one (compressor clutch relay).........
You need to have the system hooked up to the gauges to see what the readings are. You MIGHT have a clogged orifice tube, but any good A/c shop will be able to line it out
It does not have a cabin air filter.
It is in front of the radiator.
Lower passenger side of the firewall.
"Which fuse controls the fan for the ac on a 2006 Chevy silverado?"
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No, the wiring is different.