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in this example pressure = resistance
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I've never been too comfortable with the idea of using water to analogise electricity, but it does kinda work.
I see Pressure as being equal to Voltage, and Flow as equal to Current(Amps).
Going back to electricity for you Baz, there's a nice simple formula for you called Ohm's law.
It's simply E = I * R
Where,
E = Volts
I = Amps
R = Resistance in Ohms.
Thin wires have higher resistance than fat wires.
So if a thin wire has, lets say, 0.1 Ohm of resistance, then at the current's your using (forgetting your 12v supply voltage, we don't need it)
E = I (19 Amps) * R (0.1 Ohm) = 1.9 volt drop across the wire.
(That is, at the Supply end of your wire you have 12v, but at the 'scope end of your wire, the supply's 12v now appears to be 10.1v because 1.9 volts is lost in the wire)
That might not sound like much, but there's another simple formula, this time for power, which is;
P = E * I
where,
P = Power in Watts
E = Volts
I = Amps
So, the 1.9v drop across the wire becomes
P = E (1.9v) * I (19 Amps) = 36 Watts of energy lost in the wire, the vast majority of which is converted to heat, and that's a lot of heat. Remember how hot your 51 Watt Peltier got when you hooked it up?
For a wire double the diameter(not including insulation - copper only), there's one quarter the resistance, so 0.025 Ohms compared to our (randomly selected) 0.1 Ohms from the example above.
So now E = 19 * 0.025 = 0.475v dropped.
Now for the power,
P = 0.475 * 19 = 9 Watts
A quarter of the Power wasted/converted to heat.
The resistance of the wire is dependent on its diameter, as shown above, and also it's length.
A doubling in length is a doubling in resistance.
Charts are available online that show resistance per kilometre of length for various wire gauges/cross sectional area/diameters.
A rough guide to current handling of wire, is about 10 amps MAX per millimetre square of area, though I usually shoot for around 5A as a compromise between voltage drop/expense.
Wire Gauge Table - Wikipedia
Hopefully that makes sense?
It might all seem a bit overkill for what you're doing, but once you wrap your head around it it's pretty simple.
The suggested 8g wire is pretty good for the power lead wires, from supply to scope, but I would advise a smaller gauge wire, like 12 or 14 for the short interconnections between modules/switches etc. It's much easier to work with... bending, soldering, crimping etc in tight spaces.
Low voltage (thin insulation)
extremely flexible (silicon insulation) wire is available from Hobby shops in lots of pretty colours(flouro Pink anyone?) and sizes to about 10g. It's kinda expensive but much more flexible than anything you'll find at an electronics store.
Jaycar has 8g wire at reasonable prices.