What are the advantages of stranded vs solid wire?
what should i be using for prototyping circuits?
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Solid wire (24 gauge) is good for use as jumpers in solderless breadboards. Trying to push in stranded wire is frustrating. Solid wire holds its shape, so you can route wires along a path and they'll stay there.
Use stranded wire for everything else. It is flexible so it's good for cables going between a circuit board and knobs/switches on an enclosure, connecting cables between circuit boards, or any time you might have physical flexing in a wire. 24 gauge is a good all-around size for stranded too.
Non-Stranded-Easy to solder, will fit into breadboard. Trying to insert stranded into a breadboard is like trying to push string!
I prefer non stranded, in fact I have a good tip here for a cheap source.
Buy Solid Core Cat 5 or 6 Network cable, a couple of meters goes a long way...
Strip it out and you get 8 differently coloured/marked sets of good quality cable in 4 twisted pairs. Very cheap compared to buying hookup cable in small quantities, and generally better quality!
As todbot says, if you are prototyping on a breadboard then solid core is easier. Except that when you are making connections between the breadboard and something else (like a sensor, or an Arduino, or another breadboard) the wires tend to jump out of the breadboard. The solution is to use flexible stranded wire for those runs, and solder a single pin from a male header on each end to make jumpers. A short piece of shrink wrap will provide some strain relief and keep the pins from breaking off. You can also buy these jumper wires pre-made from adafruit or sparkfun, but they are easy to make.
I think, it depends on the project 100%. For example, attempting to solder stranded on to a diode... you either pop the diode or get too mush soldier. When using diodes... I always use solid core... same with capacitors etc...
Stranded works when you can crimp onto large diodes like the old Germanium types. But the newer High Output Diode does not like to be crimped... it needs all the electrons it can get.
Stranded is for 'handling' or 'the monkey principle'. If you plan to lay the wire once and forget it in a place where very little vibration occures, then solid is the way to go, the variance will not change over time as the wire oxidizes. Stranded cable because of the tiny bits of air that surround the strands, will oxidize much faster and in maybe 3 years, it will be brown and lacking conductivity.
Same with 'tinning' on small component type circuits. You don't want to change the behavior of the electrons as they flows. There is a reason we moved away from Tin wire Heavily used up until say 1985 or so... it would become brittle and in a lot of cases degrade the copper so that you would get pitting between the tin and copper. But still today, professors and engineers who earned their degrees in prior to say 1990 or 1995 are taught that tinning has a positive effect. Like Marconi invented the Radio or Edison invented the Light bulb. They teach this as 'right'. There is a reason why Cu is far away from Sn. Germanium vs Silicon... I remember my micorprocessor professor swearing Germanium will out live Silicon as the semi-conductor of the future. That is where we are with Tinning wire. Stranded vs Solid core applications for wire. If it was better then modern engineers would insist on tinned stranded cable... but we know they prefer the purist copper cable they can find for their applications.
Stranded vs Solid Core wire arguments - Stranded wire good for only applications where heavy vibrations would crack a solid core wire (I have no idea what that would be, the wire would have to be strung pretty tight)
cheaper for industry to to install and forget, there is a huge market for replacement LED's for Marine equipment because of outdated engineering data REQUIRES stranded core wires... and engineers have to use the old Germanium LED's so they can meet this standard... (wave my magic wand: "ridiculous") Maybe this made sense when we had locomomitive engines driving boats... Have you been on a boat lately, they are built like Rolls Royces... same with cars... when was the last time you sat in a new car and you thought, man I hope it holds together long enough to drive it off the lot?
How much vibration is needed (even over a long time to break a 24AWG wire?)
[I remember a study about stranded vs Solid core about which one would heat up and break faster when bent at 45 degrees but, I forget what the out come was]
[CAT 5 has been in buildings since... 1994/5 (earlier?) and is now after 15 years starting be replaced on a massive scale by CAT 7 and fiber. If stranded was better, engineers would have switched to it long ago.]
Breadboard technology - CAT 5 comes in 22AWG to 24AWG - 24AWG holds firmly unless you have plugged house wire into the holes ;-P. Or larger than 24AWG - like 20AWG wire will fit in the breadboard and 'electronic' kits come with 20AWG and will stretch out a breadboard. Expiriment - get new board and plug different size wires into holes and see which ones stretch out the holes.
When it comes to network installations (such as CAT5 in-wall) solid wire is the way to go, provided the wire is not intended to move, such as in a B&M business or a home. In the marine industry they use stranded wire for everything, as even at rest the boat moves and flexes.
Patch cables are made with stranded wire as its intended to move around.
Basically its much easier to breadboard with solid wire, but easier to prototype (solder) with stranded.
For breadboarding I use solid wire or stranded with pins attached to the ends. For wiring up a prototype board almost always stranded because it is easier to route and pretty easy to solder. In some circumstances where the wire needs to follow a particular path solid works better because it holds its shape. When soldering stranded wire it is often helpful to tin the end first then attach it to the component. Tinning exposed wire ends will also reduce oxidation. There's a good reason why tin coated wire is preferred in some applications.
Also if you're soldering heat sensitive components you can use a crocodile clip to act as a heat sink.
For prototyping, solid is easier to push into breadboards, through PCB holes, etc.
For real-life it's a combination of all the issues in all the other answers, each type has advantages & drawbacks.
Solid is used extensively for telecomms, where it gets installed/laid once & left and either wire-wrapped, soldered, or punched into an IDC terminal.
Solid is also used for fixed mains wiring; the ring main in your house wall, inside conduit in factories / offices etc.
Stranded is used anywhere there is movement or vibration; Cars, aircraft, the mains flex to household appliances, etc. as solid wire of any significant size does not enjoy being flexed very much and will fracture/fatigue, usually at a joint or connector.
In real-life applications you do need to be aware of the suitability of termination/connection methods and the fact that different connectors and processes (EG soldering, wrapping) work differently with each type & are sometimes unsuitable. For example, IDC terminals are usually designed for a specific type of solid-core wire, and may fail with other sizes or with multi-strand. Conversely, crimp terminals may not grip a single-core wire or cable but will work excellently with multi-strand.
Likewise soldering, solder can wick up the strands of a multi-strand wire and make it behave like a solid-core (I.E it becomes inflexible & can snap).
Often this stuff doesn't matter too much for hobby use, but can catch you out when exposed to the big bad world.