While using dc 12 power supply, If i connect only positive line to my electronic board and do not connect negative ,what actually happens ?
Whilst I agree with the other answers, I will point-out one exception. If your electronic board has outputs (or inputs) which are connected to another board which is connected to the negative terminal of your power supply, you might damage your electronic board. This is because current can find a path from the power supply positive to the negative terminal via the signal paths which were not intended to carry supply current.
I will add one more note of caution. When I first learned the fact that electricity required a closed path to flow, I figured that I could unwire a 240V mains plug without switching it off first. I thought "If I only touch one terminal no current will flow, right?".
Wrong. I was young and thought I was clever.
I can still remember my sense of disbelief as I was thrown across the room. I had of course failed to understand that the human body, and the ground on which it stands will also conduct current, especially where high voltages are present.
"The sound of one hand clapping".
This is usually intended as a joke answer when given BUT in this case there is some useful analogy.
Ask yourself: If you clap your hands together but only use one hand, what actually happens?
"Not connecting" one lead is the same as having a switch in that lead.
Ask yourself: If you have a circuit with a switch in the circuit and you turn off the switch (create an open circuit) what actually happens?
Charge is conserved. It cannot appear or disappear, which is why there can be no current in a disconnected wire. There will still be a 12 V voltage drop over the source, but since there is no current, it will not supply any power to the circuit. It is equivalent to hooking up 0 V source to the circuit, obviously doing nothing, and a -12 V terminal at the other end, which is disconnected, therefore also doing nothing.