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1/TR = 1/250k + 1/500k = 167k
EG 500k resistor in parallel with 500k pot gives 250k
If you use a series resistor with your pickup cable then you build up the capacitance in the coil, which makes your pickup darker. That's can also be good if you were to use 500k with singles that you pre-darken.
Tone pots are connected as a variable resistance to determine how much signal can go through the tone cap to ground. (2 terminals used.)
Volume pots are connected as a potential divider to determine the ratio of the output to pickup input signal that the amp sees. (3 terminals connected.)
The overall *DC* resistance of a 250K volume pot and a 500K tone pot is still 250K, because the DC doesn't go through the tone cap.
Generally if you want a 250K/500K setup for single coils and a humbucker, you need to add a 500K (470K is the closest normal value) resistor in parallel with a 500K volume pot when the singles are selected. It's easiest to do this on a standard Strat setup by having the upper tone control (250K) working on both single coils, with the resistor directly to ground across it bypassing the cap, and the lower tone control (500K) for the humbucker. That also means you can use different tone cap values for the singles and the humbucker, which is useful.
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