That does look like how to calculate the equivalent resistance of the divider chain as seen by the source powering it. However that's of little use for calculating a divider that will 'work' for the instructor's problem.
He's got two loads:
- 12V 6W, allegedly a CB radio
- 24V 200W, allegedly a radar
Let *US* make a further assumption - that they can operate over a +25%, -12.5% voltage range from nominal 12V or 24V typical for automotive or marine equipment fed from a Lead Acid battery.
Its obviously undesirable to overvoltage the loads and their current draw in the off or standby state may be negligible, so the unloaded divider mustn't exceed
15V at the lower tap and
30V at the upper tap.
Lets further assume that the loads are modern ones with switching supplies so will draw more current at lower voltages. At their lower operating limit of
10.5v and
21V respectively they will thus draw 6W/10.5V =
0.571A peak
*, and 200W/21V =
9.52A peak.
Also, the fully loaded current 'from' the upper tap must include the lower tap load current, even though its drawn through R2 not directly from the tap, so we must use Iload1+Iload2 =
10.1A in further calculations involving the upper tap, not the Iload2 9.52A peak current.
Lets get the upper tap done first:30V no load and 21V fully loaded is a 9V drop,
9V/10.1A =
0.891 ohms Thévenin resistance.
That's R1||(R2+(R3||Rload1)).
We've also got (R2+R3)/(R1+R2+R3)=30V/48V, and Rload1=10.5V
2/6W.
I'll let you do the math . . .
Todo: solve the lower tap, for max. 15V when the upper and lower taps are unloaded and to supply 0.571A without dropping below 10.5V when the upper tap is fully loaded. Hint: calculate the voltage at the upper tap due to ONLY the radar full load current (no radio current) and use that when calculating the required lower tap Thévenin resistance.
Conclusion:Its already obvious that the divider is going to be dissipating over one KW with both loads off, which is going to make a very effective wheelhouse heater, so the boat had better be fishing for Alaska king crab or similar where you *NEED* the heat!
I've got another rule of thumb for you: If you are attempting to draw over 1mA from a potential divider tap your design probably *SUCKS*!
* extremely unrealistic for a 12V CB radio unless its receive only, but we already suspected the instructor is a pig-ignorant ass-hat!