This one is a variant on Challenge #1, but this one has some real practical utility.

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The following circuit is provided to you:
View attachment 372292

The voltage source consists of four new AA batteries in series.

R1 is a 1 MΩ, 1% resistor.

R2 is a black box consisting of network of several unknown resistors.

You are also provided with a voltmeter that has an unknown input resistance.

Using this meter, you are to determine the value of R2. You may only measure Vab and Vbc (i.e., you may not measure Vac, but can use it if you can calculate it from the other two).

What is your best estimate of the meter's nominal input resistance?
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Here are the two measurements so that everyone has the same data to work with:

Vab = 100.7 mV
Vbc = 3.29 V

Please limit yourselves to the same conditions that the teams would face, namely that they have a basic scientific calculator and pencil/paper. They can also bring a binder with whatever reference material they want, but it is unlikely that they would have anything in it that would directly help them with this problem.

 

My best estimate is that the meter's resistance is 1 MΩ.