I trust the Car Talk guys
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Dear Tom and Ray:
Please resolve an ongoing "discussion" in our home. Should the air conditioner be turned off when you shut off the engine? My theory is that if you turn off the a/c, when you start the car, it won't cause as much strain on the battery as this question is causing here at home. Thank you for resolving this. Bill
Tom: Do you like the taste of humble pie, Bill? I hope so.
Ray: You don't need to turn off the air conditioner. In fact, it doesn't make any difference. When you turn the key to the crank position, all of the major accessories are AUTOMATICALLY turned off while the car starts.
Tom: That allows all of the battery's power to be used for starting the car. Once the car is started, the a/c, the radio, and the hot plate all come back on.
Ray: So that settles it, Bill. And by the way, tell your wife we got the 20 bucks she sent in last week.