# Electronic – Blowing resistors in parallel, in an order-controlled way

powerresistors

I'm supposed to make some questions, to gain some badges (just the excuse), so I'll throw one I've always been very curious about.

Imagine I want a set of resistors arranged in parallel to blow in a sequential and order-controlled way, just for me to admire the show, or to share it with someone else.

Look at this schematic:

I want to blow as many resistors in the set {R1, R2,… RN} as possible, as I said, in an order-controlled way. First R1, then R2, etc. I don't want to blow Rs. We can choose the values for Vs, Rs, R1, R2,… RN, the power ratings for each resistor (let's call them Psmax, P1max, P2max,… PNmax), and the maximum current Ismax that the source is able to provide. Also, assume that a blown resistor is always an open circuit.

Let's call M to the number of resistors (out of those N) that will eventually be blown.

Question: How would you choose those values, to maximize M?

I see two cases:

1) Mathematical "world", with unbounded parameters, and even making unreal assumptions such that a resistor does not blow for P < Pmax, and blows for P >= Pmax. I'm not interested in this one (because it is clear that there are infinite solutions, and with M=infinity).

2) Real-world case, with feasible values for all those parameters, and with the real thermal behavior for the resistors. This is what I'm interested in.

I know that this is a relatively complex question, and with little practical use, but I'm still curious about it, as a mathematical/engineering challenge. Aren't you? Just take your time.

Edited: Actually, let's bound Vs, so that we don't end up with HV generators. Since Olin already used 12 V in his example, let's fix Vs=12 V for all of us. Also assume a value of Ismax=100 A.