Wiring from garage panel to welder
NEC 630.11(A) may be of interest.
National Electric Code 2008
ARTICLE 630 Electric Welders
II. Arc Welders
630.11 Ampacity of Supply Conductors.
(A) Individual Welders. The ampacity of the supply conductors shall be not less than the I1eff value on the rating plate.
Alternatively, if the I1eff is not given, the ampacity of the supply
conductors shall not be less than the current value determined by
multiplying the rated primary current in amperes given on the welder
rating plate by the factor shown in Table 630.11(A) based on the duty
cycle of the welder.
Also take a look at 630.12 Overcurrent Protection.
The Owners manual (PDF) seems to contain the answer.
Wiring from service panel to sub panel
If we look at 110.14(C) in 2008 NEC, it says:
National Electrical Code 2008
ARTICLE 110 Requirements for Electrical Installations
I. General
110.14 Electrical Connections.
(C) Temperature Limitations. The temperature rating associated with the ampacity of a conductor shall be selected and coordinated so
as not to exceed the lowest temperature rating of any connected
termination, conductor, or device. Conductors with temperature ratings
higher than specified for terminations shall be permitted to be used
for ampacity adjustment, correction, or both.
Which means we'll have to check the breakers temperature rating, and the subpanel terminals temperature rating. Then we'll have to look at table 310.16 (Table 310.15(B)(16) NEC 2011), so we can determine the wire size we should use.
In this example image you can see if we're using copper, we'll use 60°C. Once we look at the table, we'll see that for 50A @ 60°C we need 6 AWG copper wire. (50A @ 75°C = 8 AWG).
110.14(C)(1)(a) basically says that if the temperature is not listed, use 60°C for circuits less than 100A. 110.14(C)(1)(b) says if the temperature is not listed, use 75°C for circuits over 100A. However, in the real world 75°C is often used for both.
No. Definitely NO way to make that receptacle switched in any way without running new wire.
Sorry.
Looks like those two switches were intended to control a fan and light separately. Notice how the black and red are in the same cable? That cable goes up to the fan/light.
Best Answer
Put a sub-panel in the garage, not a junction box. If you join 12/2 wires to the circuit, you CANNOT have more than a 20 amp breaker feeding them. If you put in a sub-panel with breakers, the 20 amp limit comes into play after the sub--panel breakers, and the feed from the main is sized for the wires feeding the sub-panel. Go bigger than you think you'll need, you won't regret it later, as most people that put in a tiny one eventually do. The sub-panel can be a "main" type panel (and could be 100 Amps, even if only fed with 30, 40, or 50 Amps), you just need to remove the ground to neutral bond. 10/3 (which has 4 wires, including the ground) would be adequate IF you are only looking for 30 amps capacity. But you actually should get individual wires and...
Put conduit in the ground, not direct burial cable. Trenches are expensive (in money or labor) conduit is cheap (in less wire damage, and the ability to replace wires later without digging again.) You need 4 wires (hot, hot, neutral and ground) and you should really consider all future uses when choosing the size of wire, rather than picking the smallest possible size. Doing it once is cheaper than doing it over.
You need to define your loads - compressors come in many sizes. The plate on the motor should give amps as well as volts; though starting them is often a bit more demanding than the running rating those provide (sometimes there is additional data on the plate which may help with starting load or required breaker size, sometimes not.) If we go minimal and assume your lighting circuit is 15 Amps at 120VAC and your tool circuit is 20 Amps at 120VAC, you're riding the hairy edge if your compressor needs more than a 10 Amp at 240VAC breaker with a 30 Amp feed, and it kicks on while your 120 tools are going. Might want to go to #8 copper or #6 aluminum for your conductors and kick up to 40Amps - default recommendation around here is actually 50A for a typical garage shop. At least choose conduit big enough to allow for that later...