I have the following setup. Note the device in the middle says P, not R, so I now how many Watts the device produces. (I'm not sure if I drew the correct symbol there)
Calculating the current resolves to a quadratic equation, which I can solve:
This gives 2 values for I, one of which will result in negative values (right?) and can be discarded.
Now, when I add another device (and then another and another), it becomes too complicated for me:
I figure there must be some general formula that I can plug into the previous one at each step.
The ultimate goal is to figure out how many devices can be added before the voltage becomes too low, considering each P and the lengths of the wires (which is what R1, R2, etc represents) Can someone figure this out?
As it turns out, working backwards is extremely easy, e.g. asking the question: "If I need a minimum of v Volts over the last device, what does \$V_0\$ need to be?" It's just a matter of adding voltages and currents.
Working forwards in the way I imagined is not doable, e.g. asking the question: "If \$V_0\$ = v Volts, what is the voltage over the last device?" This can be done with iteration.
Everyone keeps saying the voltage drop from the wires doesn't matter, but it does. With 25W devices, depending on the number of devices we hook up and lengths of wires (which can be hundreds of meters), we can get voltage drops from the wires that are over 10% of the voltage drops from the devices. 2 or 3 Volts per wire is significant in our situation.
Thnx for your help, everyone!