A single resistor R is connected across a 10 V battery and 0.01 A flows. A second identical resistor R is then added after the first one along the same wire, and the current drops to 0.005 A. What would the total resistance be if ten identical resistors R were connected this same way, one after the other?

1. With one resistor, R = V/I = 10 V / 0.01 A = 1000 ohm. 2. With two resistors connected one after the other, R = V/I = 10 V / 0.005 A = 2000 ohm, which is exactly 2R. 3. Doubling the current path's length by adding a resistor 'after' the first, one after the other, doubled the total resistance. 4. This confirms the resistors are wired one after the other, so N identical resistors give a total resistance of N times R. 5. For ten resistors, the total resistance is therefore 10 R. 6. 5 R would arise from an arithmetic slip halving the count instead of using all ten resistors. 7. R divided by 10 is the rule for identical resistors combined a different way, not one after the other, so it does not apply here. 8. R squared is not a resistance-combination rule that appears anywhere in this reasoning. _Source: OpenStax Physics (CC BY 4.0), Ch 19 "Electrical Circuits", section 19.1 Ohm's law_