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I'm working through examples for an Arduino capacitance meter and the ones I've seen give the known resistance of the RC circuit as 10 kilohm. It's my understanding that we could use "any" known resistance. Is there a reason that 10 kilohm is commonly selected?

Two examples that both use 10 kilohm: https://www.circuitbasics.com/how-to-make-an-arduino-capacitance-meter/

Here's a response to a Quora question about finding capacitance that also uses a 10 kilohm resistor with a 9 V battery: How can I determine the capacitance of an unknown capacitor?

There are others.

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    \$\begingroup\$ Viable implementations typically use multiple resistors connected to distinct IO pins and auto range until they find one which gives a good time period for the test capacitor connected. \$\endgroup\$ Nov 22 '20 at 18:51
  • \$\begingroup\$ @ChrisStratton I just looked up auto-ranging. I didn't realize that was done with fancier multimeters. Thanks for the tip! \$\endgroup\$ Nov 22 '20 at 20:09
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It is usually desirable to maximize the resistance in order to be able measure relatively small capacitance values.

The ATmega328P datasheet says:

"The ADC is optimized for analog signals with an output impedance of approximately 10 kΩ or less.

.. and then goes on to describe the effect on the sampling time. The leakage current is also a potential issue.

That does not mean that one could not use less or more resistance in some given situation, with careful analysis, but it's a reasonable starting point.

For example, to measure a 10,000 µF capacitor, 10 kΩ may be too large (\$\tau\$ = 100 seconds). However, if you go too low in resistance then the output resistance of the GPIO pins will start to affect the time constant.

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    \$\begingroup\$ Ahah! This is a bit of gold, thank you. I've bookmarked the link. I can't seem to upvote just yet due to my newness, but I do appreciate the help. (Your edit added even more value. Thanks for the pointer indicating impact on the time constant.) \$\endgroup\$ Nov 22 '20 at 17:23
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    \$\begingroup\$ @ElizabethWoodward the upvote privilege comes with 15 reputation, and I think your questions are really well-researched enough that you gathered that amount of reputation now :) have fun! \$\endgroup\$ Nov 22 '20 at 17:27
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    \$\begingroup\$ Thanks, @MarcusMüller. I'm truly grateful for this community and the insightful help everyone's providing. \$\endgroup\$ Nov 22 '20 at 17:34
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It's just that 10 kΩ make sense for the voltages/currents and capacitances (or: charge, which is just capacitance·voltage) and timescales used. That sets the order of magnitudes. You need to realize that the way you measure things only works if the measurment device (the ADC of the microcontroller, here) has only small effect on the observed phenomenon. Pick a much larger resistor, and a significant amount of the discharge current will flow through the ADC, compared to through the resistor. Pick a much smaller one, and your microcontroller will be too slow to measure smaller capacitors' discharge time.

Why exactly 10 kΩ? That's a bit arbitrary.

There's "series of preferred numbers", from which things such as resistor values are taking. 1, 1.2, 1.5, 1.8, 2.2, 3.3, 3.9, 4.7, 5.6, 6.8 and 8.2 times any power of 10 are easy to buy (it's called the E12-series). Other values do exist, too, but are rarer.

Since this is a measurement device, you'll want to buy a resistor that's the specified resistance with very little error – up to 5% error are "standard" resistors, but you can get resistors with less than 0.1% error specification. However, these are "special purpose" and more expensive, and also not available for just any value.

You'll find that 1.0·10⁴ Ω is a preferred number, and you can get precision resistors with a nomimal 10 kΩ value.

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    \$\begingroup\$ Thank you. Order of magnitude makes sense. Unfortunately, I can't seem to upvote just yet. I do appreciate the help. \$\endgroup\$ Nov 22 '20 at 17:21
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Digital engineers tend to use 10 kΩ for every job that doesn’t absolutely require something different. A 10 kΩ resistor will draw 50 µA at 5 V or 33 µA at 3.3 V, which gives acceptable power consumption and reasonable immunity from interference.

You may also notice that digital engineers use 10 or 100 nF decoupling capacitors, where 33 or 47 nF would be fine.

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    \$\begingroup\$ Downvote for the 'us and them' digital engineers stuff, implying some categories of ignorance. Good engineering includes reducing BOMs to their fewest variants to simplify purchasing, stock, pick/place etc across your boards. So using common values where its calculated to be inconsequential is good engineering. Hence the popularity of certain values. \$\endgroup\$
    – TonyM
    Nov 23 '20 at 19:23
  • \$\begingroup\$ I am a digital engineer (mostly) \$\endgroup\$
    – Frog
    Nov 24 '20 at 5:04

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