Actually one should get in the
habit of occasionally checking switches, connectors and wiring for heat - it's usually a sign of too low a wire gauge (high resistance) or failing connectors and switches (bad contacts -> higher resistance).
I should get in the habit too. (Might have saved a burnt foot when my 30 year old floor mounted dip-switch melted!)
The above AND your resistor heat issue are solved by 2 basic formulas, namely Ohm's Law V=IR, & the Power formula P=VI.
ie, V=IR means the voltage across something equals its resistance times the current thru it. (Volts, Ohms, Amps)
P=VI means the Power dissipated by something equals the Voltage across it times the current (I) thru it. (Watts, Volts, Amps)
Note that a load can
convert that power - eg, a tungsten lamp converts ~5% to light and (wastes) ~95% as heat. A resistor is 100% heat.
So your (say) 1k resistor.
Assume 15V (typical worst case for a 12V system).
V=IR. Divide both sides by resistance R and we get V/R = I.
So I=V/R = 15V/1,000R (where I use "R" instead of having to specially paste in the Ω symbol (since I couldn't be bothered learning which of the Alt-
whatever codes is appropriate for hatemail (html) pages etc)).
So I = 15/1000 = 0.015A = 15mA.
How much heat is that?
P=VI = 15V x .015A = 0.225W.
That's ~.23W which is just under 0.25 = 1/4 Watt.
So a 1/4W resistor should be fine (especially since we over-estimated a little by using 15V instead of 14.4V or 14.2V or 13.8V or 12.7V etc - those being typical alternator else battery voltages).
I'd prefer a 1/2W resistor but that may be an
old's cool thing when 1/2W resistors were physically more robust than 1/4W. However. a 1/2W resistor can dissipate twice the heat that a 1/4W can, and it should run cooler. (Resistors can be quite warm or hot at their rated power.)
Can you do the same calculations for a 300R resistor?
BTW - resistors come in "preferred values" and ratings eg, 1/8W, 1/4W., 1/2W, 1W, 2W 5W, 10W, 20W etc, and Ohmages that are "multiples" based on 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68 & 82 - eg, 10R, 100R, 1,000R etc 120R, 120k etc. (That's the traditionally common "E12" range so named because there are 12 "base values". There are also E24 & other ranges. And "multiples" and "base values" are not the correct terminology - I forget that sort of
basic stuff!)
1/2W used to be the "standard" resistor
size unless higher power was required or miniturisation was important. But modern 1/2W resistors are the same size as 1/4W resistors were a few decades ago (yes, I was (emotionally) shocked!).
I can do the 300R example, but I do it quicker than above.
I happen to remember that P = VV/R or IIR (aka V**2/R or V^2/R, or I^2R etc) where VV =
V-squared usually written as V-
superscript-2 or V², but often as V**2 or V^2 or V-e2 for mathematicians etc with poor Alt-keyboard memories.)
So for 300R & 15V, P = 15V x 15V / 300 = 225/300 = 0.75W,
... hence a 1W resistor (or larger).
Maybe you can check that?
FYI - the VV/R & IIR comes from combining V=IR & P=VI.
ie, P=VI = (IR)I - IIR (I x I x R).
or V=IR; divide both sides by R to get V/R = I, so P=VI => P=V x (V/R) = VV/R.
[Yes, I remember my Year-3 maths!)
POST-EDIT - that VV is V V (meaning V times V or VxV etc), it's not a double-U (W) (or double-V as some logical languages call our W).
Incidentally, it is the P=IIR version that is the "easy key" to the
heat check theory.
Ignoring current, we see that P
is proportional to R, ie, the heat given off (by switch or connector contacts or a wire) is proportional to its resistance. Bad contacts are a higher resistance as are thin wires, hence R increases so P - the power or heat given off - increases.
Alternatively, for P=IIR, if the R is constant, then P is proportional to I² (I x I).
So if P is whatever at current I, then doubling the current means the new "P" increases by (2I) x (2I) = 4I, ie, the Power/heat quadruples.
If 3x the current, it's 3x3 = 9x the heat.
And I'm not sure why I went into that - it isn't that relevant for your resistor, but it shows how increasing the current has a much larger effect on the heat generated. Doubling the current requires 1/4 the resistance for the same heat output or wastage; 3x required 1/9th the resistance, etc. That impacts wire gauges, component ratings, heatsinks, etc.
Oh well, another OldFart
crazy ramble....