I was myself concerned about the rating of controllers (technically, these are 'infinite switches' https://en.wikipedia.org/wiki/Infinite_switch).
Opening the range (with breaker OFF of course!), I examined the controllers, all of which had the same rating and ID codes -- despite that one of the burner elements was an 8", and all the others were 6".
Again, ALL the controllers were the same.
Going to a parts website to find the electrical rating for this infinite switch (controller), I found it rated for 3600 Watts, 240 Volts, 15 Amps.
This seems to be good for any of the coil sizes and numbers.
Yes, the different coil numbers will have a different resistance (see pictures). But, naturally they would, since they are rated for different wattages (remember, W = I^2 * R, that is, Watts is the current squared, times the resistance. The voltage is the same (240 Volts) and more current will flow through the LOWER resistance, so the lower resistance coil is the higher power one).
However, the controller appears to be quite capable of handling the difference (at least the ones on my Tappan range cooktop).
And, judging from all the many dozens of numbers of infinite switches on the parts supplier crossover list, they don't appear to be 'finely tuned' to the burner size or coil number.
I replaced an 8", 4-coil, with an 8", 5-coil. And, I replaced a 6", 3-coil, with a 6", 4-coil. They both work well. They both seem to heat faster and more evenly, and will bring pots to boil quicker on high. They are also 'flatter' on the bottoms of pots and pans.
So, I would (safely) open the range or cooktop, read the numbers off of the infinite switches and look them up to determine the ratings.
Please tell me if I am missing something.
The only thing I can think of is that the infinite switch might 'pulse' more, as the larger rated burners will reheat quicker.
But, again, the infinite switches are rated for 3600 Watts, 15 Amps, 240 Volts. So this is not out of the listed rated capability of the switch -- at least for power.