015 Why can’t ohmmeters work together?

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For ease of discussion, let’s call the Digital Multimeter (DMM) on the left DMM A, and the one on the right DMM B.

To measure resistance, DMM A actually drives a constant current I0 through its terminals. It then measures the potential difference V0 across its two terminals. Based on V0, the DMM reports the resistance R0.

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What happens when DMM B joins in the fray? Since DMM B will also be driving a constant current I0 through its terminals, the total current will be 2I0,  resulting in a pd of V0=2I0R0 across R0. But both DMMs have no idea of each other’s presence and assumes a current of I0 through R0. They thus (wrongly) reports a resistance of 2V0/I0 = 2R0.

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When DMM B’s range was increased to 2 MΩ, it expects a larger resistance, so it drives a smaller current of 0.1I0 instead. This results in a total current of 1.1I0 through the resistor, resulting in a pd of V0=1.1I0R0. DMM A, which assumes a current of 1I0, reports a (less inaccurate) resistance of 1.1R0. But DMM B, which assumes a current of 0.1 I0, reports (an even more inaccurate) resistance of 11R0.

The moral of the story is, when using the DMM as an ohmmeter, it must be the only EMF source in the circuit. If not, the readings will all be screwed up.

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