A 1.00 ohm, a 6.00 ohm and a 13.0 ohm resistor are connected in parallel across a 12.0 V battery. What is the total resistance of the combination?

1. For parallel branches the reciprocals add, so work with 1/R for each branch. 2. 1 / 1.00 ohm = 1.000 per ohm. 3. 1 / 6.00 ohm = 0.1667 per ohm. 4. 1 / 13.0 ohm = 0.07692 per ohm. 5. Adding gives 1.2436 per ohm. 6. Inverting that sum gives Rp = 1 / 1.2436 = 0.804 ohm, which is below the smallest branch as it must be. 7. 1.24 ohm is the sum of reciprocals left uninverted, the commonest slip in this calculation. 8. 4.11 ohm is what the 6.00 ohm and 13.0 ohm branches give on their own, leaving the 1.00 ohm branch out. 9. 20.0 ohm is the series total for the same resistors, which cannot describe a parallel combination. _Source: OpenStax College Physics (CC BY 4.0), Ch 21 "Circuits and DC Instruments", section 21.1 Resistors in Series and Parallel_