Final answer:
The combination that provides the minimum resistance is having all three resistors - 3 ohms, 6 ohms, and 9 ohms, connected in parallel, as this parallel configuration results in the least possible resistance value.
Step-by-step explanation:
To find the minimum resistance combination using a 3 ohm, 6 ohm, and 9 ohm resistor, you want to put all resistors in the configuration that results in the least resistance. This will be achieved when all resistors are connected in parallel since the equivalent resistance of a parallel combination of resistors is always less than the smallest individual resistor.
When resistors are connected in parallel, the total (equivalent) resistance becomes lower because current has multiple paths to travel through, hence decreasing the overall resistance. Mathematically, the resistance total (Rtotal) for resistors in parallel can be found using the reciprocal formula
1/ Rtotal = 1/R1 + 1/R2 + 1/R3... and so on.
Therefore, the correct choice is: All three resistors - 3 ohms, 6 ohms, and 9 ohms, should be connected in a parallel combination.