Resistors in Series and in Parallel

Ordinary circuits contain many elements; it often simplifies analysis to reduce the circuit to a simpler state with fewer elements.
Connecting elements in series forces all current to pass through each element.
Connecting elements in parallel permits current to pass through only one element.
Several resistors connected in series have equivalent resistance
```
            R(eq) = R1 + R2 + R3 +  ....             (in series)
```
The equivalent resistance is larger than each individual resistance.

Several resistors connected in parallel have equivalent resistance

              1      1     1     1
            ----    --- + --- + --- + ...            (in parallel)
            R(eq) =  R1    R2    R3

The equivalent resistance is smaller than each individual resistance.

We can use these rules to build resistances of almost any value we need from just a few different types of resistors.