Tax code followed by 0?

My tax code is followed by a zero (i.e. 543L 0). I put this in one of those tax calculators online, and it came out not charging me any income tax. I took the 0 off to see what it would do, and the income tax was taken out. I just started my first job in the UK back in Jan. of this year (still there) and had the 0 before, and wasn't charged income tax, but now that the new tax year has started, even though the 0 is still there, I'm now being charged income tax. Can anyone explain this difference to me? The only thing that's different is that the number before the L is different now (it's a higher number now than it was before).

Thanks!

Not sure what the 'O' is for.  The 543 number is higher than it used to be because the standard personal allowance amount (£5430 now) was increased with the new tax year.