If we have a collection of six 1.0 Kohm resistors. What is the smallest resistance you can make by combining them?

**Answer 1**

Resistors in parallel will always equal less than the smallest resistor in the group.

Since all six resistors are equal value, you can use a short cut.

Rtotal = 1000/6 = 166.666 Ohms.

If they are different vallues, use the following:

Rtotal = 1/((1/R1)+(1/R2)+(1/R3)+(1/R4)+(1/R5)+(1/R6))

Rtotal = 1((1/1000)+(1/1000)+(1/1000)+(1/1000)+(1/1000)+(1/1000))

Rtotal = 1/(.001+.001+.001+.001+.001+.001)

Rtotal = 1/.006

Rtotal = 166.6666 Ohms

**Answer 2**

It would be very convenient if every circuit you could just pick and choose your conditions. Real life you need to allow for real values. IF all the resistors were the same value, all connected in either series or parallel then you could calculate based on the power rating and known total power. But if the values were random, it comes down to the total power is equal to the sum of the powers dissipated. If you have two resistors of different values and the same voltage across each (say when they are in parallel) then the lower resistance value will dissipate more power than the higher one. Obviously, that resistor will have to be rated at a higher amount than the other.