DC Metrology
DC Electric Circuits
If a voltmeter is to be used to directly measure the voltage of an unknown source, it must first be calibrated so as to ensure an accurate measurement:

What is the minimum number of points along the meter’s range that it needs to be calibrated at, given the assumption of perfectly linear response?
If a voltmeter is to be used to measure the voltage of an unknown source, as a differential indicator only, what is the minimum number of points along its range that it needs to be calibrated at?

This voltage divider should output half the battery’s voltage between points A and B:

However, if you perform this same experiment using a real voltmeter, the measurement obtained with the meter will be substantially different from what should be there, based on a prediction of ^{1}/_{2}E_{battery}. Explain why the voltmeter registers as it does. What is it about this circuit that causes the measurement to be so far off from the prediction, when we know full well that other voltage divider circuits we’ve constructed do not exhibit any significant error?
The following voltmeter circuit avoids problems of “loading” when measuring highresistance voltage sources. Describe how to operate this circuit, and how loading error is eliminated by using such a potentiometric instrument:

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