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You need to first understand the way the resistor is "put together". There are various different types, and you didn't specify. For example, there are simple bulk resistors where everything in the electrical path lies on a straight line. In a wirewound resistor, the resistor element is wound in a spiral around a cylinder. Or you could be talking about a resistor in an Integrated Circuit (IC) or on a thick-film hybrid circuit. You could be talking about a small "chip" resistor that goes onto a PCB. You need to be more specific to get a more specific answer.

The first thing you should determine is if the resistor is actually open, or if you simply have a bad connection to the resistor. Is it soldered to something? If so, use an ohmmeter equipped with pointed probes to check for connection on either side of both of the resistor's solder joints, if possible. If this is not possible (such as in the case of a surface mount "chip" resistor), you have to consider the solder joint as part of the resistor in the investigation.

In fact, you should keep in mind that failure of a solder joint is MUCH more likely than simple failure of a resistor, unless the resistor has had too much current passed through it. Resistors tend to be mechanically more robust and reliable than solder joints.

If the resistor was electrically overstressed (too much current, causing too much power dissipation/heat) the point of failure should be fairly obvious. There will be black, carbonized material at the failure point. You may need an optical microscope to see it, and it could be internal. There may be other external signs, such as bulging or discoloration that are not as obvious.

If the resistor is not truly open but merely very high resistance, it may be possible to thermally image the fault location. Care must be taken to not pass through too much current and make the fault worse (unless you only care about the fault's location and not its cause).

A high resolution x-ray can be used to image and find electrical opens in some types of resistors. It may also be possible to use more advanced tools such as Acoustic Tomagraphy, but that is rarely justified for using on a resistor that has become open. There are simpler, cheaper techniques that will give good results. The big advantages to x-ray and Acoustic Tomagraphy are that they can be done non-destructively.

If it is a true electrical open, you generally expose the conductive element by stripping off the exterior chemically, or by cross-sectioning the device. Opens can then usually be spotted with simple optical microscopy. If the defect is too small, a Scanning Electron Microscope (SEM) can be used to image it. If one lead of the resistor is grounded, the un-grounded part of the resistor will quickly accumulate a charge and start to "glow" in the SEM, exposing the site of the open.

Remember, if you couldn't verify that the solder connections to the resistor were OK, you have to consider them as possible points of failure in the analysis.

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Q: How do you isolate fault in a open resistor?
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