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For the sake of expirementing, as far as I have tested (with simulators online) connecting an ohmmeter in parallel with the single component in a closed circuit with a generator short circuits, concluding that the resistance of an ohmmeter is ideally 0, right?

I have found no conformation nor information about this online, but what made me wonder even more is an ohmmeter acts as a voltmeter that exports power, and voltmeters having ideally $\infty$ power, so an ohmmeter having no resistance didn't make much sense, perhaps because it is the source of the energy it does not require resistance? Current leaves and enters through it, doesn't pass through it. I have absolutely no idea how resistance works with components producing energy so bare with me here! Like, does a generator have resistance as well (well a simple google search says yes), and why? No electricity goes through it I think. And perhaps ultimately an ohmmeter and a generator don't relate in terms of resistance, sharing the common aspect of producing energy doesn't affect that.

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    $\begingroup$ I don't think it's obvious what "ideal" means for an Ohm meter, but I'm pretty sure that your average, bench-top Ohm meter (a) is only intended to measure the resistance of a component that has been isolated from any circuit, and (b) delivers power to the the component when it is being used as intended. $\endgroup$
    – Solomon Slow
    Commented Oct 11, 2021 at 21:36

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An ohmmeter is

  • supplying power to a circuit and
  • comparing the voltage across two legs of the circuit (a reference leg and a test leg)

If the resistance differs too much, then it will be difficult to compare the voltages. You want to be able to tell the difference between a high resistance and an open circuit.

For a modern digital multimeter, it does this by starting with a very high resistance and seeing if the measured resistance is detectable. If not within limits, it tries a lower resistance, continuing until it can make a reasonable reading or until it cannot drop any lower and measures it to be a (nearly) zero resistance.

So one way to imagine an ideal ohmmeter would be one that had an internal (reference) resistance that exactly matched the test resistance, so that a voltage or current comparison would be identical through the two portions of the circuit.

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I suppose an 'ideal' ohmmeter could be modeled in ideal circuit theory as an ideal $1\,\mathrm{A}$ DC current source in parallel with an ideal voltmeter.

A resistance $R$ connected to this parallel combination would have a voltage across of $R\,\mathrm{V}$, i.e., the numerical reading on the voltmeter equals the resistance of the resistor.

Such a parallel combination would have an infinite equivalent resistance rather than zero ohms.

And yes, an open circuit would necessarily give an infinite resistance (voltage) reading so this is not remotely physical.

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What is "ideal?" It might depend on how the Ohm meter works.

One kind of Ohm meter would impose a constant voltage, $V$, on the device under test (DUT), it would measure the current, $I$, and it would calculate the resistance, $R=V/I$.

What is the resistance of an (an ideal) ohmmeter?

An ideal voltage source doesn't have "resistance" per se, because it does not obey Ohm's law. But you can define its impedance, $Z=\Delta{}V/\Delta{}I$, which, like resistance, is measured in Ohms. The impedance of an ideal voltage source is zero, because no matter what happens with the current, it's voltage remains constant: $\Delta{}V=0$.

That's probably pretty close to how a lot of Ohm meters actually work, but the ideal case has a very practical problem: For very small resistances, the current and power delivered to the DUT would be huge: In fact, it would increase without bound as the resistance of the DUT approached zero. One practical fix for that would be to put an arbitrary, small resistance in series with the voltage source, and account for it in the calculation. But that would limit the precision with which very small resistances could be measured. So, less than "ideal."

Another kind of Ohm meter would drive a constant current through the DUT, and measure the voltage. This could give arbitrarily accurate measurements for very small resistance values, but the "ideal" case would be a terrible choice for high resistance values because the voltage would increase without limit as the resistance increased. In fact, with no DUT at all, there would be a steady electric arc between the probe tips, because the current must be a non-zero constant.

What is the resistance of an (an ideal) ohmmeter?

The impedance of an ideal current source is "infinite" (strictly speaking, it's undefined) because $\Delta{}I$ always equals zero.

What's the resistance of [a practical] Ohm meter?

I don't know. I don't know what compromises are accepted by the engineers who build practical Ohm meters. I'd guess that they tend toward the constant voltage model, but there could be various tricks to get more accuracy and/or to limit the amount of power delivered to the DUT in various resistance ranges. A "smart" Ohm meter might even switch between modes depending on what it senses.

If the ideal is either zero or infinity, then I suppose that the reality must be somewhere in between.

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  • $\begingroup$ Hi Solomon, is it the case that impedance is defined as $Z=\Delta V / \Delta I$? In my recollection, as an EE old timer, the quantity on the right hand side is an approximation of the so-called dynamic resistance or small-signal resistance. Impedance, on the other hand, is a complex quantity defined as the ratio of the voltage and current phasors associated with a circuit element in AC steady state. $\endgroup$
    – Alfred Centauri
    Commented Oct 13, 2021 at 1:09
  • $\begingroup$ @AlfredCentauri, I never was a real EE, even though I may have played at that role on a few occasions during my career. I guess I used that word because I maybe misunderstood diagrams like the one on this page. I'm not so sure about "dynamic" or "small signal" resistance though for this particular case. What if I replaced "impedance" in my answer with "effective series resistance?" $\endgroup$
    – Solomon Slow
    Commented Oct 13, 2021 at 2:19

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