What is the resistance in a parallel circuit with resistances of 2 ohms 4 ohms 6 ohms and 10 ohms?

In a parallel circuit, the total resistance is the inverse of the total of 1 over the value of the first resistor plus 1 over the value of the second resistor. Said another way, if you take 1 over the value of R1 plus 1 over the value of R2, and then take 1 over that, you will find Rtotal. So let's do that. 1/10 + 1/2 = 1/10 + 5/10 = 6/10 1 divided by 6/10 = 10/6 = 1 2/3 ohms for the total resistance. As a quick check, in any parallel network where a group of resistive elements are all connected in parallel, the total resistance will be less than the value of the smallest one. The smallest one in this case is 2 ohms, so we are good to go by that simple check.