Since they are in series, they will have the same current. The power dissipated in a resistor (or anything else) isActually I just realized that this won't work with 50Ω and 100Ω resistors as my current limiting resistors.
For the 50Ω resistor the power dissipated in it will be (.15)(.15)(50) = 1.125 watt which is far greater than the 1/4 watt it is rated for.
For the 100Ω resistor, the power dissipated would be (.082)(.082)(100) = .67 watts (which still exceeds its rating by almost a 1/2 watt).
I would need something in the vicinity of a 500Ω resistor so the current would be ~18mA and the power dissipated across the 500 Ω resistor would be (.018)(.018)(500) = .16 watts
I think what it boils down to is that for this to work the power rating of the load resistor NEEDS to be less than the power rating of the current limiting resistor by at least half.
Or does it? Any suggestions on what I should use for my load resistor and what I should use for my current limiting resistor?
P = I·V
But using Ohm's Law it can be written as either
P = (V/R)·V = V²/R
or
P = I·(I·R) = I²R
Since they have the same current, the latter form is the one that makes the most sense to use. So the ratio of the powers in the two resistors is
\(
\frac{P_1}{P_2} = \frac{I_1^2R_1}{I_2^2R_2} = \frac{R_1}{R_2}
\)
Since I1 = I2.
Thus, if you use a 100Ω resistor and a 10Ω resistor, the 100Ω resistor will be dissipating 10x the power as the 10Ω resistor.
Another demo you might consider is show that with a 100Ω 1/8 W resistor and 12V you get about the expected 1.2 A (the meter on the 10A range should have a sufficiently low burden resistance to yield a good measurement) and that the resistor either burns up or gets extremely hot since it is dissipating 10x the power it is rated for.
Then use Ohm's Law (and a tiny bit of math) to show that putting 10 resistors in series to make a string and then 10 strings in parallel will yield an effective resistance of 100Ω. Then demonstrate this by showing that it still draws 1.2 A from your supply, but now the resistors don't even get warm since each is dissipating about 1/10 of the power it is rated for.