i just recently finish all of the dlc's and i've gone back to the main game and i searched the brotherhood of steel safehouse and found the tesla cannon, how good is it once it's fully repaired?

not as good as it was in FO3 i believe. The tesla-beaton prototype is the strongest variant in NV and it hits prety hard but consumes ammo quite rapidly

Tesla Cannon? EEEHHHHHH it does 80 damage when full repaired and maxed in EW skills and has an after effect of 20 damage /a second for 2 seconds, so it does 120 damage total, it eats Electron Charge packs, and takes 5 per shot, with an ammo cap of 30, so basically, you can fire it 6 times before reloading.

It also has a crit chance of x2, so any decent crit build would probably enjoy this weapon, as it adds another 40 damage.

Now...if you want me to crack my knuckles and whip out a spell for you as one of the Weapon Wizards, Here's the max damage output you can do with this thing, without sneak attack criticals

With Max Charge Ammo, it does 120 damage +20/2seconds
With Better Criticals and Just Lucky I'm Alive, the crit damage is now 40x2.25=90 damage per shot,
When having 10 Luck, Recon Beret, Finesse, your crit chance is 40%, 60% with that Critical chance Magazine and Comprehension perk taken.

so in total, you have the ability of doing 250 damage per shot for just 5 Maxed ECPs

You're much better off with the Unique version.

It does 90 damage, and 25/2 per second DoT effect.

it has a x2 critical chance and 45 crit damage.

With Maxed Charge ammo, and with the calculations from before, you're capable of doing 286.25 damage per critical shot.

This is overall meh, considering the downsides:

It takes 6 ECPs with the Prototype instead of 5, and it has 24 ammo capacity, meaning it only fires 4 shots before reloading. Not only that, but it doesn't have it's AoE splash effect like before, so you have to be precise with this weapon..Luckily, the prototype only has 0.08 spread.

Final conclusion:
As long as you don't miss your shots, and you got the caps for ammo,crafting for Max charges, and for Weapon Repair kits, it's a good weapon. It all depends on your taste, honestly.