We can combine resistors in series, and in parallel.
Resistors in series add values:
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 + ... +
But this is formula a pain in the neck to work with. A slightly simpler
transformaton, for two resistors, is:
Rtotal = (R1R2)/
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