Cable Size

<sigh> British Standard 7671.

I'll just offer a hint (because I don't want to look up the appropriate tables myself).

There are two criteria to consider: the current must be less than the rated ampacity of the wire / cable (and insulation) to avoid a fire hazard, and the voltage drop must be such that the load can tolerate the voltage drop and / or relevant codes.

In your case, the voltage drop consideration will be the driver (well, at least under US codes (NEC: National Electric Code) it would be). IIRC (and I don't), I think the code calls for no more than a 3% voltage drop under load.

So, you need to:

• determine whether the 3% limit is what you must design to (if not, what is the design criteria), then
• determine (using Ohm's Law: E=IR) how many ohms of total resistance will cause a voltage drop corresponding to the limit that you must design to, and finally,
  
• find a table of wire sizes and associated resistivity (per foot, or per 100 feet, or per meter, or whatever) and then determine what size wire is required to have a total resistance less than or equal to the total resistance allowed (from the previous step) (you need to consider the total resistance of both wires, and, at least in the US, you will need a third (grounding) conductor along with the two current carrying conductors.

Is this a temporary or a "permanent" installation? If temporary, there may be exceptions of some sort that might allow you to reduce the wire size determined.

no its parmanent installation .I select cable 14 awg its current carrying capacity is 32 A

and 8.282 ohm/km,

so V=IRx2(neutral and phase)

so voltage drop=2x4.55 x8.282x350/1000 volts=26 Volts

but is this voltage drop is acceptable in engineering?

if ok i will use this if not please help me,

see here.

http://www.youtube.com/watch?v=umDr0mPuyQc

No, almost certainly not. It doesn't meet the 3% criteria for one, and if it is an incandescent light, powering it at 84 volts (110 - 26) will produce much less light (and probably red) than it would at 110 volts. (That drop is over 20%, isn't it (26 / 110).)

(If it is some other kind of light (HPS, CFL, I'm not sure what will happen--perhaps some of those can work at a much lower voltage (like 84 volts), but I suspect not, and I suspect there is some maximum voltage drop specified by your codes that you must not exceed.)

As per the your specs

Rated Vol= 110V

Rated PW=500W

Length=350V

As per IEC voltage drop must be less than 2.5%

you must select 3CX 4 Sqmm Cable considering cables voltage drop(mv)/amp/meter is 10mv

sudip