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For the past couple of weeks I have been losing power occasionally to half my house. My central AC goes out, half my kitchen, living room and my kids' rooms. There are no tripped breakers though.

I have noticed that when the AC finally turns back on, so does everything else. It will be that for a while, then all of a sudden everything goes off again. Once I get the air conditioning running, everything powers up again. My house is only 13 years old and have never had this problem.

What is the likely cause of the issue, and what can I do to fix it?

If you're in the US, my guess is that you're losing one leg of your incoming power somehow. Power comes into your home as split phase 240 volts - there are two 120V "legs" that are 180 degrees out of phase. Typically one leg goes to each side of the breaker panel. I bet if you trace the circuits that are down, they all go to the same half of the panel. When the air conditioning, which uses both legs, turns on, it bridges the gap and backfeeds power to the other half of your house.

Now, how you're losing a leg of your power is another question entirely. This is likely a utility problem and you should call them ASAP. The utility will check things out and if it is on their side of things then they will fix it for free. If they determine that the problem is in your panel, they will let you know and then you need to call an electrician for a repair. This is an unsafe condition and can cause all sorts of problems, so get it checked out ASAP.

You are losing a hot from the pole

In North American {or multiphase European} service, When you lose all your 240V* loads and about half of your 120V** circuits, that means you have lost a leg of power. Here is how most North American panels are laid out, if your lost circuits fit the pattern, that confirms it.

That problem may be around the main breaker in your service panel. It may also be inside your meter pan. However it is most likely out at the electric pole or somewhere in between pole and meter. That is the power company's bailiwick and they fix that for free as part of the service.

What's happening is when the 240V air conditioner cycles on, it is unable to run because one of the poles is disconnected. However, a motor trying to start is quite similar to a dead short, and this has the effect of shorting the two poles of power inside your panel. For instance if pole L1 lost power, all the breakers on broken L1 are now getting L2’s power via the air conditioner. This is no good thing!

You can get this diagnosed for free by calling the power company and reporting an outage. They will also treat it as an urgent matter.

Turn off your 240V* loads, this can damage them.

You don't see any bold headlines on this answer because it isn't another problem: same problem but with the neutral wire broken. In that case it would be a true emergency. Your 240V* loads would work, but your two 120V** loads would have either too-high or too-low voltage (the two voltages adding up to 240V* ***). The too-high voltage can melt appliances and start a fire. The advice would be the same, we'd just be screaming it.

* in Europe and Eurostyle service on 5 continents, this number is 400V. In NYC and parts of Central America this number is 208V.

** in Europe etc. this number is 230V.

*** in Europe or NYC, the voltages won't quite add up to the higher number, because of 3-phase weirdness. There, power is supposed to be a triangle with neutral in the middle. This failure causes it to float around.