Simply put. By filing away at the resistor body, you can change the resistor's value in an upwards direction.

First some History:
My Farther use to work at a defence research place called WRE back in the 50s. (Weapons research Establishment.) It was a time when the Woomera rocket range was in full swing. There were several problems with putting electronics on rockets in those days. Firstly the range of components were limited. The best resistors you could get were about 5% tolerance. Most were 10% and even 20% tolerance. And as such the range was limited to the E12 range. In fact there was no other range. These days we take for granted that we can get the E24 and E96 ranges of resistors. With available tolerances of 1% and even 0.1% if you wanna pay for 'em. The range refers to the number of resistor values per decade. E12 has 12 values per decade naturally enough. Chosen to give the best possible choose when cascaded together to form other values. For example. 10, 12, 15, 18, 22, 27, 3K3, 39, 47, 56, 68, 82. 12 values in all When 5% resistors were common, the range was extended adding another 12 values in between. Useful values like 20, 43, 51 and 75 would be added in between. When 1% became the norm the E96 range was added in resistors with even tighter tolerances. 96 values per decade. Still the E96 range is less common. Most of the toy shop style chain store electronic hobbyist retailers still only stock the basic E12 component these days but as usual I digress.

Back in the 50s and early 60s large 10% tolerance carbon film resistors were the norm. Now the thing to remember is that these resistors were relatively stable temperature wise but it was a manufacturing tolerance that was imposed. Now the problem with launching electronics on rockets is that they take off at about 50 G. That's 50 times the gravitational force of just standing at sea level. So if you've got bulky trim pots on your circuit boards, this G-force tends to rip the components from the board. Plus in those days telemetry wasn't all it is today so much of the data had to be retrieved from the rocket after it crashed back to earth. A small radio transmitter had to survive the crash so that retrieval teams could locate it anything up to 3,000 Ks down range.

All this meant that bulky component like trim pots were out of the question mostly. And remember that back in the 50s they also didn't have the little cermets and the like we take for granted these days.

The resistor it self:
A carbon resistor is a carbon based resistive material. Cylindrical in shape and bonded at each end with some wires. Then coated and colour coded. The resistance depends on the density and composition of the resistive material. These days they call them carbon film. That is that they coat a film of this material onto a small cylindrical substrate which forms the resistor. It means that resistors can be made very small as compared to the old days. More modern and stable Metal film resistors are similar in construction but are almost reminiscent of a wire-wound resistor. Except they don't exhibit the inductance of a wire wound. Essentially speaking though, the more dense the material, the less resistance. The trade off is that the less material there is, the lower the wattage handling capability of the resistor. I'm not entirely sure how they rate this but I would assume that as the composition of the resistive material changes to get different ranges of values, so would the amount of resistive material need to be changed in order to maintain a constant power handling factor. I would assume that at some values of resistance, a standard quarter watt resistor would actually handle more than quarter watt. But the entire range of power handling would be rated such that no resistor would handle any less than quarter watt. This would change from manufacturer to manufacturer I would think. This factor will become significant later on.

How to Customize a Resistor:
Assuming you have a standard carbon film resistor at hand, place it between two alligator clips on your multi meter probes thus.

Then with a small needle file, file through the coating on the outside of the resistor till you reach the resistive material inside. Then gently file away the resistive material and you'll notice the resistance climb. Of course you can only make the value rise so you need to choose a resistance value lower than your target value. When you reach your desired resistance value, coat the filed out area of the resistor with some nail polish. Where would the electronics industry be without nail polish. I'm sure using it on nails was an after thought. :)

It is important to note that you don't need to use much pressure on the resistor. Partly because it's relatively easy to file past the target value but also because you don't want to place too much mechanical stress on the resistor. You need to be gentle with the resistor. Take it slowly and note that the contact of the file it self might temporarily change the resistor's value. Giving a false reading. You have to file a bit then remove the file and check the reading. Do this as you go as often as possible.

Anyway it's that simple. If you had a 2K2 resistor and you needed a 2K3, you can simply file it up to the desired value. Even really strange values that would not exist even in the real world are possible. Like say 1.234K. When doing the calculations for a filter for example the standard approach is to do the calculation and find the best fit components. Often has been the case where the best fit components in E12 render a filter response that is nothing like the response one needs. Not any more. You can just file up the exact weird value resistor and make a perfect filter.

But wait there's more:
Juergen Haible <Juergen.Haible@nbgm.siemens.de> Had this idea to add.

Trimming (filing) in circuit would be the big deal. Imagine tuning a filter bank. Measure capacitors, then do some calculations and select resistors, or combinations of 2 resistors in series. Lot of measurement and calculation involved. If you can trim the resistors in the living circuit, just feed in a sine with the right frequency and file until the amplitude at the output reaches the peak. Same as with trimpots, only that you have better long term stability and tempco.

This is a great point. By filing in circuit you could measure the response of the circuit until it comes up to the exact conditions you need for the exact response. But there is the concern about getting conductive filings into the circuit board which may cause problems or damage. You would have to be careful here and blow or brush the filings from the board to prevent this from happening.

Customizing Metal films:
Now the conventional wisdom here is that you can't customize a metal film. Only carbon film resistors can be customized. But this is not necessarily so. I have successfully trimmed up quarter watt Metal film resistors as well. The resistive material in metal film resistors is tougher than that of carbon. Carbon is like filing through some kind of chalk. Metal films are like filing through aluminium. Because you need to file it more you can be more accurate. But be warned. robin bussell <robin.bussell@lucent.com> has this concern.

Well metal films are (or at least *were*) ceramic tubes, coated on the outside with the resistive film. Sometimes , for the higher values I suppose, this film would have a helical groove etched into it so that the resistive film actually ended up being like a ribbon wrapped round the tubular substrate. Filing one of these at the wrong angle or in the wrong spot could give you an open circuit fairly quickly.. so you can file 'em but sometimes you might get a bit too much extra resistance all of a sudden :-)

So it's important to note. You should only file it in one spot on the resistor. You should never file around the resistor.

Finally as mentioned before, a resistor has a power rating. The standard size and most commonly used in small signal, low voltage electronics being one quarter watt. When you file the resistor, you are actually lowering the power rating of the resistor as well. Ever so slightly may be but it's worth noting. If your circuit required a resistor right on tolerance, you could be in trouble.

Finally Robin also points out thusly:

What you're doing is essentially the same as the automated 'laser trimming' you see boasted about quite often.. I wonder if we can come up with a suitably bombastic term for filing... something like "individually hand trimmed by frictive attrition" :-)

This has been used in a number of electronic devices. Most notable precision trimmed Analogue and digital converters, multipliers and digital audio controls. Basically resistive elements are laid out in silicon. Before the dye is mounted in the IC package it is inserted into a testing and measuring machine. The resistors are hit with a laser which burns off layers of the resistors until the value comes up to the optimum. Thus pre-turning the circuits before they are packed and shipped.

So when you need a custom resistor, get your little bastard out and start filing.

Be absolutely Icebox.