### Author Topic: Exercise 1.9 from "The Art of Electronics" (Third Edition)  (Read 1940 times)

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#### ajlenze

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##### Exercise 1.9 from "The Art of Electronics" (Third Edition)
« on: September 03, 2016, 07:02:22 pm »
I've been working through some of the exercises in the new third edition of "The Art of Electronic", and exercise 1.9 is the first one that I'm not sure of my answer.  Here's the exercise:

"The very high internal resistance of digital multimeters, in their voltage-measuring ranges, can be used to measure extremely low currents (even though the DMM may not offer a low current range explicitly).  Suppose, for example, you want to measure the small current that flows through a 1000 M ohm "leakage" resistance (that term is used to describe a small current that ideally should be absent entirely, for example through the insulation of an underground cable).  You have available a standard DMM, whose 2 V dc range has 10 M ohm internal resistance, and you have available a dc source of +10V.  How can you use what you've got to measure accurately the leakage resistance?"

My thought was to connect everything in series, but I have two problems with this solution:
1.  For the leakage resistance varying +-10% around 1000 Mohm, the voltage measured by the DMM only changes by about 20mV (90mV for 1100 M ohm and 110mV for 900 M ohm).  Can the DMM detect this small of a voltage change accurately?
2.  The formula for the leakage resistance is 10M*((10/VDMM)-1), where the 10M multiplier is the DMM's internal resistance.  This means that accurately calculating the leakage resistance depends on how accurately you know the DMM's internal resistance.  How accurately do you typically know a DMM's internal resistance?

Is there a better way to solve this problem?  Thanks in advance for any help you can give me.

#### Simon

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##### Re: Exercise 1.9 from "The Art of Electronics" (Third Edition)
« Reply #1 on: September 03, 2016, 07:35:46 pm »
It does indeed sound like the internal resistance of the DMM is used as a shunt or rather as part of a resistor divider. A bit crude but then I am often surprised at the things I read in the art of electronics and wonder why it is so popular.
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#### JPortici

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##### Re: Exercise 1.9 from "The Art of Electronics" (Third Edition)
« Reply #2 on: September 03, 2016, 08:00:18 pm »
as you thought, you connect the two in series.
+10VDC is precise
the internal DMM resistance in the 2V range is 10M

so the voltage you read when the two are in series is indeed 10M * I leakage, so you know ileakage.
the Rleakage will be (10V - Vdmm) / I leakage
the error from this measurement will be determined mainly by the DC source precision and the DMM internal resistance precision. if you need a rough estimate you can use the absolute values, if you need to know the error you have (or you can measure) the error for each of the parameters, in the real world. just remember that you can not achieve absolute precision, only good enough precision.

@simon we did all sorts of things like this in high school, in measurement lab

#### rstofer

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##### Re: Exercise 1.9 from "The Art of Electronics" (Third Edition)
« Reply #3 on: September 04, 2016, 01:01:04 am »
Perhaps the thought is that the current flow is objectionable.  It isn't so terribly important how much current flows, simply that current flows at all.  Just getting a rough estimate of the order of magnitude may be all that is necessary for troubleshooting purposes.

#### Zero999

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##### Re: Exercise 1.9 from "The Art of Electronics" (Third Edition)
« Reply #4 on: September 05, 2016, 06:24:38 pm »
It does indeed sound like the internal resistance of the DMM is used as a shunt or rather as part of a resistor divider. A bit crude but then I am often surprised at the things I read in the art of electronics and wonder why it is so popular.
I've done a similar thing before to test the leakage current of a BJT. Although it is crude, it's certainly a good way to measure tiny currents, without having to buy specialist equipment.

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##### Re: Exercise 1.9 from "The Art of Electronics" (Third Edition)
« Reply #5 on: September 06, 2016, 04:33:15 am »
its a nice solution to measure R leakage

Smf