I have a storage shed that I'd like to run power to. My source is a former air conditioning circuit that I was told was 20 Amps, however when I took off the cover to the box out side, I saw 2 black wires and a ground wire. The breakers were removed due to the serviced being rerouted thru the main box near the meter. Can I still use this as the source if I reinstall a 20 amp breaker? And shouldn't it have a white wire?
The original circuit was a 240 volt circuit, so a grounded (neutral) was not required. Because of this, you only have two ungrounded (hot) conductors.
If these wires are part of a multi-conductor cable, and not individual conductors. The Authority Having Jurisdiction (AHJ) may allow you to reidentify one of the conductors, so that it can be used as a grounded (neutral). Check with your local building department, to determine if this is allowed.
Otherwise you'll have to pull a grounded (neutral), or new cable with a grounded (neutral) conductor.
You'll also want to check the gauge of the wires that are in place, as they're likely 10 AWG. While there's no problem using 10 AWG conductors on a 20 ampere circuit, you might find that the wires are too large to attach to devices (receptacles). If this is the case, you'll have to use smaller pigtails to connect the wire to devices. Check the markings on the device, to determine the acceptable wire gauge.
By code, using a colored conductor as a neutral is not allowed, as these are the only allowable of identifying a grounded conductor (neutral):
2014 National Electric Code
200.6 Means of Identifying Grounded Conductors.
(A) Sizes 6 AWG or Smaller. An insulated grounded conductor of 6 AWG or smaller shall be identified by one of the following means:
(1) A continuous white outer finish.
(2) A continuous gray outer finish.
(3) Three continuous white or gray stripes along the conductor's entire length on other than green insulation.
(4) Wires that have their outer covering finished to show a white or gray color but have colored tracer threads in the braid identifying the source of manufacture shall be considered as meeting the provisions of this section.
You said the "breakers" were removed-- this leads me to believe you had a 240V circuit there which did not require a neutral; therefore, both blacks were intended to be hots. In that scenario, it is not a code violation.
Will what you have work electrically with a single 20A breaker? Yes. Is it 100% up to code for a circuit with a neutral? No.
There's a good chance you can still use it. I'd guess that one of the two black wires is a neutral, does it have a piece of white tape or white paint on it?
With luck everything's kosher going back to the main panel and you can just have a GFCI breaker installed in the air conditioning box and tie in the buried cable.
If not, as long as the cable is good and goes back to the main panel, you should be able to get it hooked up without any major expense.