The only test equipment you would ever need for the repairs mentioned in this web site would be a digital multimeter (or DMM). The only procedures that require you to use a multimeter are the ones involving the power board or the plasma display panel.
With a digital multimeter you would be measuring either DC voltage or resistance (continuity).
If you are to measure DC voltage, make sure your multimeter has a maximum range of 300 volts or more. If the meter can be set to more than one DC voltage range, set it for a range that is higher than the voltage you are about to measure. If it has an auto-ranging capability for DC voltage, you can select that setting.
The only electrical resistance measurements that would be necessary are for simple continuity. In other words, the precise value of the resistance is not important. What matters is whether or not you have a low-resistance electrical connection between two points, or a "short circuit".
A multimeter is a handy thing to have for other reasons. For example, you can use it to test batteries. Just set the meter to read DC voltage, place the probes on the ends of any D-, C-, AA- or AAA-size battery, and read the voltage. A fresh new battery will give a reading of over 1.6 volts. If it measures less than 1.3 volts, the battery is far from being fresh and would be a likely candidate for replacement.
Be sure to read the instructions that come with the multimeter, especially the safety instructions. And, do not set the multimeter to an ampere (A), a milliampere (mA) or a microampere (µA) scale if you intend to measure a voltage, as this could destroy your multimeter.
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