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That may not sound like much, but even when your target is only 6000, it means you can be anywhere between 5400 and 6600 and still be fine. That's a big range, and it only opens up more the more you are generating. For example, at 12k, you have 1200 worth of tolerance, so you can generate anywhere between 10800 and 13200.
I usually only use the resistors when I'm booting up after a maintenance shutdown or if I've screwed something up such that I'm hitting a big spike over the target for some reason.
Yup, I was doing the same thing as you at first and trying to hit it as exact as possible. Once I realized that you just need to be fairly close, it made a lot more sense.
First of all, the water in the primary coolant loop is quite hot, so it acts as a battery of sorts: if the core isn't generating enough heat to match the amount of electricity you are supplying, the primary coolant loop will cool down to make up the difference. Of course, if you dip into your primary circuit heat too much, the steam generators will stop producing steam, so there's a limit to this, but it gives you some short-term adjustability, and some additional time that you can keep generating electricity after fully inserting the control rods.
But in addition to that (and much more powerful, actually the main point here), there's also the fact that temperature affects the reactivity of the core (colder is more reactive), so the reactor actually powers up when it is better cooled and powers down when it is worse cooled, which means that the cooling loops actually act as a throttle for the reactor, and that gives you long-term adjustability. You still have upper and lower temperature limits that you can operate the reactor in (overheating vs. not being able to heat the steam generators), so you still need to adjust the rods to have temperature leeway in either direction, but you can exercise a considerable degree of control just with the coolant pumps.
This latter factor lead to a rumor among non-technical staff in the US Navy that the nuclear carriers were insanely faster than their published speeds. Other steam-powered ships would have to build up heat in the steam circuit slowly, because the amount of heat generated didn't depend on the amount of cooling, and they could only shove oil and air into the boilers so fast. If they tried throttling up the turbines to a higher steam flow rate than the boiler fires could support, they wouldn't heat the steam up fast enough and would start carrying water into parts of the circuit that weren't meant to have water in them, and would have a Very Bad Day. The CVNs could just start using more steam and the whole temperature-dependent reactivity bit would cause the reactor to automatically start putting out more heat to replace the heat that had been taken out. So while they weren't *faster* than other ships in their task force, the CVNs had very impressive acceleration. They'd start flight ops and ramp right on up to 35 knots, while all their escorts were still building up steam. So sailors on destroyers would see the carrier disappear over the horizon, and they wouldn't catch back up until the carrier had finished flight ops, and they figured "We can do 35 knots, and the CVNs leave us in the dust. They must be able to do 45 or 50 knots". In reality, the carrier just got up to 35 knots very quickly, but wasn't really faster than the escorts at full speed.