Don't worry about feet & meters (meters are a bit longer than yards, and 3m = ~10'), but I'll use that Merkan AWG table anyhow...
Do you have any suggested or target max voltage drops - ie, <0.5V from MPPT to battery; <1V from panels to MPPT; less than 1V from battery to outlets at 5A etc?
I won't do it now, but then I can redo those calcs - maybe in very verbose form so that you can later DIY by substituting new values (distance, current, etc).
It is "simply" (ha!) an exercise on Ohm's Law, ie: V = IR.
aka "the voltage drop V along something equals the Current (I) going through it TIMES the total Resistance of it".
(Units are Volts, Amps & Ohms. Though often V, mA & kΩ are used - the milli- and kilo- cancel each other out.)
[ BTW: Ω = Ohms, but many use the "R" instead because we & I couldn't be bothered looking up and pasting the Ω symbol, or writing it, etc. And
we know when the R means Ω as opposed to as in V=IR. BTW, in V=IR, the IR is short for I*R or IxR (I times R). And I is the symbol for Current (Amps). And if V=IR, then R = V/I where / means "divided by". That's obtained by dividing both sides by "I", ie:
V = I * R
hence V/I = I/I * R
hence V/I = R (because any number divided by itself is one - aka "the I's cancel".)
]
The modification is that you are using lengths of cable.
But a cable of certain size has a resistance per length.
EG - in that linked table, see the "Ohms per 1000 ft." column.
For simplicity, 13G is 2.003 Ohms per 1000 ft. Lets call that 2 Ohms per 1,000', and I'll use "R" instead of "Ohms".
So 100' = 0.2R. 10' = 0.02R. 1' = 0.002R = 2mR (milli-Ohms).
That's just dividing each side (2R = 1000') by 10 each time.
EG - if you had 30', then that's 2R x (30/1000) = 2 x 0.03 = 0.06 Ohms. (check: if 1' = 2mR, then 30' - 30 x 2mR = 60mR = 0.06R. Phew!)
So at 10 Amps, V = IR = 10A x 0.06 Ohms = 0.6.
So 30' of 13G at 10A will have a 0.6V drop.
That means 1.2V (2 x .6) taking the ground path into consideration (ie, it is then 2x30' = 60' at 0.002R per ' = 0.12 Ohms. 0.12 Ohms x 10A = 1.2V. (Great - checked ok again!)
Rats! I started my "not now" rant already.
But can you follow that? Or maybe the notation is confusing eg, 2 Ohm / 1000' = 2 Ohms divided by 1,000' which is like saying "2 Ohms
per 1,000'.
More later - including other answers to your last....