With the switch set for the Neck pickup, the Bridge controls have no effect on the sound - as you would expect. With the switch set for the Bridge pickup, the Neck controls have no effect on the sound. Put the switch in the middle, and turning either volume control down to about 1 or lower shuts off the signal from both pickups, no matter how loud the other one is set to.
Wha? Huh? Is it broken? No. It's a feature. (Which I spent the better part of a Sunday understanding.)
FACT ZERO: the pickup-> volume control -> tone control -> selector switch circuits are wired in parallel.
FACT ONE: The volume controls are potentiometers, not variable resistors. A potentiometer has three tabs: input, output (attached to the variable control) and ground return. A variable resistor has two tabs: input and output. This matters. Were we to put a current in via the output tab (sounds odd, but no harm will result), a potentiometer provides two circuits: one to the input tab, and one to the ground return tab. Each one of those has a resistance: Rin and Rgnd, and Rin + Rgnd = 500k ohms always, at least on Les Pauls.
This will be important in a couple of paragraphs.
FACT TWO: don't forget the most important circuit in any guitar, the one out to the pre-amp, which takes a louder copy (that's what amplifiers do), and lets the original current go back into the guitar return circuit. That amplifier circuit has a resistance, Ramp.
Back to the Selector Switch. When it is in the centre, both output lines are connected.
Read that again!
When the switch is in the centre, both the output wires from the volume controls are connected. The output tab of the Neck pickup is connected to the output tab of the Bridge pickup.
So by facts ONE and TWO, the output tab of each volume control sees three circuits:
1) to the amplifier, resistance Ramp
2) to the other volume control and out through the ground return, resistance Rgnd
3) to the other volume control and out through the input tab, resistance Rin
This is where the magic happens. As we turn down (say) the Bridge volume, we are increasing Rin and therefore decreasing Rgnd because that's what happens in a potentiometer. Keep turning the volume on the Bridge down, and Rgnd will become close to and then much lower than Ramp. At which point hardly any current is going to the amplifier, because it is following the path of least resistance, Rgnd, and the guitar sounds as if it's been turned off.
Which was required to be proved.
This does not happen with Strats and Teles because the selector switch is before the pots in a Fender, and the connection to the pots is made by the same wires from the switch frame, no matter what position the switch is in.
(Some gnarled old electrical engineer at Gibson no doubt took one look at the mock-up of the Les Paul circuitry and said "Very nice, if you want one pot to ground through the other at low volume when the switch is in the middle." And everyone shook their heads and thought, there goes Old Joe again. Until it happened.)
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