Can my Fluke 87 handle this?

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If the requirement is for an analog meter that is 20K per volt or higher, yes, your Fluke will handle it quite well. Your Fluke most likely is a fixed 10M ohm impedance and will not load most circuits you are trying to measure.

Older analog meters could give false readings by 'loading' the circuit that was being measured especially in the lower voltage ranges. Analog multimeters have different impedances depending on the range setting. For example if an analog meter was 20K ohm per volt, and if it were set to a 100 volt scale, the input impedence would be 100 times 20K or 2M ohm. However if it was set to a 1 volt scale, the input impedance would be only 20K ohm and that could load the circuit and give false readings.

Most digital multimeters (like your Fluke) have a fixed 10M ohm (or higher) input impedance so they don't have a loading effect on the circuit being measured.
 
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On occasion, the reading on the chart or diagram includes the loading effect of the meter. So a DVM is likely to read a slightly higher value in such cases. But for most circuits the difference is negligible.

If you know the circuit impedance, it's easy to calculate that difference. Of course, meters with low sensitivity not only might read lower but also could disturb the circuit operation, depending on impedance level.
 
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