I am using protoboard to build something. The current that will go into the protoboard will be ~3 to 4 Amps. So searching how to make things better, instead of using 1 "cell" everytime to make α "conduit"from one element to the other and make a circuit, I think of using two, so as to expand the size of the "conduit"and reduce the resistance. Can this work? Has anyone tried it?
Perhaps use suitable hookup wire soldered along the path of pads or "cells" to act as a conductor or "conduit"?
A photo would help.
There are thumprules for that, used by circuit board layout designers. Something like: for a 6 micrometer thick copper folia and 1 mm wide You can run 1 Amp. Maybe it was 3 Amps… Check it up.
Building prototypes on protoboard, a common approach to carrying more current, is to build up a "bead" of solder along the track.
I call that "baking". Doing it along the conductors works resonably well but to bridge the gap to the next conductor easily deposits tin where You don't want it to be and there's a pool of tin to suck up.
"Filleting" might be another description.
I use a combination of Paul__B'a approach and insulated wire. I'm not as neat as Paul, but, in my defence the flying wires are temporarily connecting a pot for debug only . For long runs I strip solid telephone or network cable and 'spot weld' solder it along the path.
IMHO the "current rating" of a solder trace - doubled or not is not really quantifiable. Dave Jones (youtube) did some testing of this some years ago. If current rating is critical, then I would be tempted to solder in a copper conductor of suitable size, then I won't go far wrong. Solder isn't consistent and is only as good as it's weakest puddle, Yes there looks like there might be enough solder there for a "few" amps, but to say it will carry 3 amps but not 5 amps is, in my book, highly subjective and requires many considerations - not least personal level of risk aversion. It's a prototype and as such I would expect things to go wrong. So personally - given that that situation- I would not worry about it too unduly, I would follow Big Clive's (Youtube again) example and use an "explosion resistant pie dish" if I was worried. If it was something that was to be used by someone else or to run unmonitored or outside my immediate direct control I personally would not be using proto board anyhow, but that's just me. The "fun" in this hobby is often finding out the hard way!
Please dont think I'm suggesting anyone should abandon common sense or ignore safety, I'm most certainly not - quite the opposite in fact. :o
As a general rule I suggest to take special care about currents like 3 Amps and up. Make the supply line short, not criss crossing the board and do the same for the output to the load.
Amps, maybe switched causes some electrical fields that it's advicable to keep as faar away s possible from the sencitive low power circuitry.
Your devices will start burning "the next day".
alex5678:
This is what I mean...
That sort of board with the square pads is of course, designed for the solder bridging technique, the round pads are not as easy to bridge and do not make as wide a path.
blewtobits:
I'm not as neat as Paul, but,
Hey, don't confuse a photo I pulled from the 'net with what I do myself! 
I don't even recall (yet) using that sort of protoboard - I generally use (generic) Vero. 
Is that sort of constructions with 3-4 (max 6 Amps) Amps on protoboard need a fan or something for cooling?
As I understand it and I'm just throwing in my twopennethworth here, there are people here far more qualified than me to comment, the short answer is that it's not really possible to state an absolute value because there's too many variables to confidently answer the question to the accuracy requested. Will it safely carry 3 amps? - Probably. 4 amps? - Less probably.
The long reason behind that answer is; my experience has drawn me to the understanding that current carrying capacity is all about the ability of the conductor to lose the heat it generates in conducting that current. Two primary issues are pertinent. The attributes that cause heat to be generated, such as resistance (conductivity, current rate, eddy currents, cross section area, etc) , and attributes that allow generated heat to be dissipated (ambient temperature, surface area, thermal conductivity etc. ). All attributes can be manipulated, for example, increase conductor CSA, u/exchanging the conductor to one with a higher copper content, heat sinks, fans, liquid nitrogen cooling etc. Each have different degrees of effectiveness.
There are equations that can be applied to calculate all this, but they rely on accurate figures for things that can be difficult to determine on a hobbyist workbench. Which is why it's not really possible to determine a definitive answer in the limitations of photos in a forum chat.
I can think of 2 alternative methods.
One is to use tabulated data such as those published by cable manufacturers, which is the basis of my first suggestion of using known cable size which cable data can be applied to.
The other is experimental trial by error. Passing increasingly larger currents through a soldered trace in a controlled manner until the temperature exceeds that you feel comfortable with. (In an explosion proof pie dish). The bigger the bang the greater the satisfaction