My (soon-to-be-replaced) air conditioner is frequently tripping the circuit breaker in my apartment. What can I do to prevent this?

I have a 14,000 BTU AC in my living room. When it gets turned on, everything else must be turned off: TV’s, computers, microwaves, etc. Sometimes, on a hot day, even with everything else off, the circuit breaker still gets tripped. I don’t know much about electrical stuff, but the circuit breaker switch that is always getting tripped is labeled “20A.” My AC (if I’m reading it correctly) is “115V, 12A.” My guess is that the circuit breaker trips whenever more than 20 amps of current are going through (which makes me wonder: just how much power does a TV or a computer use?). In any case, will replacing the circuit breaker for a higher one fix the problem or just increase my risk for blowing up the whole thing? My circuit breaker has 4 switches in all labeled “20A” and it’s always the same one being tripped; I wonder if plugging my appliances into other outlets will have any effect on this problem.

I rent the apartment and I’ve asked the super to look into it, but he claims it’s the old wiring in our (pre-war) building and nothing can be done. In our lease agreement, we pay an extra fee for each air conditioner unit we have (currently two). But is the landlord really holding up his end of the agreement if turning those air conditioners on forces me to sit in the dark?

To top it all off, the AC causing all the power problems is just about dead. I’m going to be buying a new one in the next week or so. This has me wondering if I should be trying to get one that uses less power (if it exists) or buying a couple of smaller ones instead.

Correct me if I’m wrong: Wouldn’t three smaller ACs use less power then two really big ones? And yet, according to my lease agreement, I would be required to pay an extra fee for the third unit. I’m going to be contacting the landlord about this, but I’d like to educate myself on the issue before starting any trouble.

Any information on circuit breakers, amps, etc., would be really appreciated.