The best answer to this is: Read the fine print on your credit card agreement.
What is common, at least in the US, is that you can make any charges you want during a time window.
When the date comes around that your statement balance is calculated, you will owe interest on any amount that is showing up as outstanding in your account.
To revise the example you gave, let's say Jan 1. your account balance was $0. Jan. 3rd you went out and spent $1,000.
Your account statement will be prepared every XX days... usually 30. So if your last statement was Dec. 27th, you can expect your next statement to be prepared ~Jan.24 or Jan. 27.
To be safe, (i.e. not accrue any interest charges) you will want to make sure that your balance shows $0 when your statement is next prepared.
So back to the example you gave--if your balance showed $1,000... and you paid it off, but then charged $2,000 to it... so that there was now a new set of $2,000 charges in your account, then the bank would begin charging you interest when your next statement was prepared.
Note that there are some cards that give you a certain number of days to pay off charges before accruing interest... it just goes back to my saying "the best answer is read the fine print on your card agreement."