## Combining Resistors

We can combine resistors in series, and in parallel. Rtotal = R1 + R2 + ... + Rn

Resistors in parallel work a little differently. The general forumula for computing resistance in parallel is: #### 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn

But this is formula a pain in the neck to work with. A slightly simpler transformaton, for two resistors, is: Rtotal = (R1R2)/ (R1+R2)

Even this, though, is not very usable. A handy rule of thumb for resistors in parallel is:

#### 2 equal R's in parallel total R/2. 3 equal R's in parallel total R/3, etc.

As an example of how elegant this rule of thumb is, consider this arrangment of resistors: To analyze it, take the two 10k's in parallel first -- they combine to make a 5k. Now you've got two 5k's in parallel, for a total of 2.5k ohms. Simple!

Here's another example, which makes the rule of thumb seem even more clever: = = Instead of reaching for your calculator, think of the 5k as two 10k's in parallel. Now you've got three 10k's in parallel, for a total of 3.3k.

We have one other useful trick: spotting the dominating resistor. Remember that resistor tolerances are usually about 10%, so anything that changes our total resistance by less than 10% can be safely ignored.

In practice, this means we can ignore the effect of Rsmall in this case: And we can ignore the effect of Rbig in this case: Assuming that Rbig is more than ten times the value of Rsmall.