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A voltage across series resistors divides up the total voltage across each resistor. The voltage across each resistor is based on it’s percentage of the total resistance. The voltage divider circuit fragment uses the voltage at one of the nodes (connection), in relationship to ground, as a signal.
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Fixed resistors of equal value are easy to calculate.
2 equal value resistors will have half of the supply voltage across each of them. If 12V is across both of them, then there will be 6V where they connect (node) as long as little to no current is being pulled from the node.
3 equal value resistors wired as a voltage divider will have 2 output nodes. If 12V is across all of them, then the node with 2 resistors on the high side and one on the low side will have 4V in relation to ground. 1/3 of the resistance is on the low side (headed towards ground), therefore that node is 1/3 of the supply voltage (12V x 0.333 = 4V).
Whereas the node with 1 resistor on the high side, and 2 on the low side, has 2/3 (0.666) of the resistance between it and ground. Therefore it is at 12V x 0.666 = 8V.
Again, that is just a signal voltage for circuitry, or measurement tools, that responds to voltage without drawing much if any current. The more output current that there is, the more that the node voltage will be thrown off.
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