# Resistors

## Series and Parallel Resistors

Resistors are paired together all the time in electronics, usually in either a series or parallel circuit. When resistors are combined in series or parallel, they create a **total resistance**, which can be calculated using one of two equations. Knowing how resistor values combine comes in handy if you need to create a specific resistor value.

## Series resistors

When connected in series resistor values simply add up.

*N resistors in series. The total resistance is the sum of all series resistors.*

So, for example, if you just *have to have* a 12.33kΩ resistor, seek out some of the more common resistor values of 12kΩ and 330Ω, and butt them up together in series.

## Parallel resistors

Finding the resistance of resistors in parallel isn’t quite so easy. The total resistance of *N* resistors in parallel is the inverse of the sum of all inverse resistances. This equation might make more sense than that last sentence:

*N resistors in parallel. To find the total resistance, invert each resistance value, add them up, and then invert that.*

(The inverse of resistance is actually called **conductance**, so put more succinctly: the *conductance* of parallel resistors is the sum of each of their conductances).

As a special case of this equation: if you have **just two** resistors in parallel, their total resistance can be calculated with this slightly-less-inverted equation:

As an even *more special* case of that equation, if you have two parallel resistors of **equal value** the total resistance is half of their value. For example, if two 10kΩ resistors are in parallel, their total resistance is 5kΩ.

A shorthand way of saying two resistors are in parallel is by using the parallel operator: **||**. For example, if R_{1} is in parallel with R_{2}, the conceptual equation could be written as R_{1}||R_{2}. Much cleaner, and hides all those nasty fractions!

## Resistor networks

As a special introduction to calculating total resistances, electronics teachers just *love* to subject their students to finding that of crazy, convoluted resistor networks.

A tame resistor network question might be something like: “what’s the resistance from terminals *A* to *B* in this circuit?”

To solve such a problem, start at the back-end of the circuit and simplify towards the two terminals. In this case R_{7}, R_{8} and R_{9} are all in series and can be added together. Those three resistors are in parallel with R_{6}, so those four resistors could be turned into one with a resistance of R_{6}||(R_{7}+R_{8}+R_{9}). Making our circuit:

Now the four right-most resistors can be simplified even further. R_{4}, R_{5} and our conglomeration of R_{6} - R_{9} are all in series and can be added. Then those series resistors are all in parallel with R_{3}.

And that’s just three series resistors between the *A* and *B* terminals. Add ‘em on up! So the total resistance of that circuit is: R_{1}+R_{2}+R_{3}||(R_{4}+R_{5}+R_{6}||(R_{7}+R_{8}+R_{9})).