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My car has sat for more than a week without charging the battery at all. As long as your alternator system is working correctly, no modern car should require a battery charger for only a weeks worth of inactivity.
I believe TIS puts the line (for showrooms) at leaving a car sitting with no charging activity at 6 weeks. So a week should be fine. In theory. So long as you don't make it mad. Be sure to leave it some chips or something so that it doesn't feel neglected and get mad.
if I take vacation for a week w/o running car, should I charge before, after, or both ?
Have left other cars sit for a week or more -- one nearly 3 weeks -- while I was out of town. All were fine with one exception. With one car I left an OBD2 code reader plugged in. When I got back battery so low it would not crank the engine.
But that really was not due to sitting unused a week, but sitting unused with a parasitic electrical load.
I have to add that in all cases the battery was in good condition. And the cars had received enough use before being left unused a week+ that the battery was topped up. A battery starting out with a low charge and with some miles/time on the battery may not fare as well being left to sit a week.
Besides making sure to use the car a good amount before parking it I like to park it with a full fuel tank.
Be sure when you park the car all electrical loads are removed. Don't do like I did and leave something plugged in to the car. And lock the car which puts the car's electronics in their lowest power mode. Has never been a problem with me because my cars are parked some distance from my residence, but if the car in question has keyless/comfort access store the keys far enough away from the car that the car's security system is not able to contact the keys.