Why do DMM leads have such high impedance?
They don't. Well, good ones don't...
What is the resistance of your DMM test lead? Mine (UT61E) lead is 0.6ohms. I recall in other comments, the commenter said his test probe is merely 1.1ohms; another comment in another thread has his leads at as high as 2.1ohms. I recall in a youtube video by Martin Lorton on constant current drain, while discussing the need of his 1ohm-50W resister, he said his CrocClip cable is 0.5ohms. The GatorClip cables (5 pairs) I got all measure in the 0.5ohm range.
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That really brings my puzzlement to the forefront. How come production DMM cables have such high impedance? My not very well made DMM clip-probe is 0.02ohms. Why is the production DMM leads in the 0.5ohms range? That is a good magnitude difference!
They have such a high resistance because they are crap.
A special place is reserved in hell for the makers of the UT61E test leads. Mine failed, in a very nasty way - resistance would randomply jump between some dozen mohms and some dozen ohms. Drove the continuity tester nuts...
So i retired them, cut off the banana plug and then cut that POS open. Turns out the wire had a jacket (is that the right english word?) crimped onto it (that is good), and that went into a hole in the metal body of the banana plug.
Now the problem was this: all that was securing the connection between the jacketed wire and the plug body was a round indent (1 to 1.5 mm) pressed into the banana plug body over the hole, and the molded plastic around it (see image). That means the jacketed wire end can wiggle slightly in the somewhat larger then the jacket hole - piece of crap, going to go bad sooner rather than later. If they had compressed the plug metal along the whole length of the hole, from both sides, it might actually have worked reliably.
The resistance between the probe tip and the other end of the wire was constant and good, but I don't trust that anymore.
So I got myself some Fluke leads and hope these are properly made.