As a self-assignment for troubleshooting the Hameg oscilloscope, I needed to measure kiloVolts. The world agrees that you need to arrange a resistive voltage divider using an high impedance (10 Mohm) voltmeter.
For example if your voltmeter has an input impedance of 10 Mohm you need a 90 Mohm resistor in series to obtain a 1:10 ratio:
(kV)------/\/\/\/\/------[Voltmeter]------(GND)
90 Mohm 10 Mohm
I looked for suitable resistors at home and I found 4x 10 Mohm and 5x 5.27 Mohm, all 10% or more. So theoretically I could reach 66 Mohm which gives about 1:7,6 ratio. The chosen voltmeter can measure 500V, that's up to 3800V "input".
Since it is hard to accurately measure high resistances and their value may change with voltage I decided to determine the ratio with an experiment.
Given that the input impedance of an instrument might be unknown or different from the spec sheet, I empirically found the ratio of different voltmeters I own. First measure a DC voltage V1 using the voltmeter alone. Then measure again the same source adding the big resistor in series, you get V2. V1/V2 is the ratio of that resistor using that voltmeter at that voltage range.
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| A high-Z probe for HV. |
I repeated the experiment at higher voltages, like 80V and 300V, to observe that the ratio increases 1-2% with applied voltage (300V vs 10V). I settled to 1:8.02 for my setup.
I completed the build with a label on the probe that reminds its usage and characteristics.
IMPORTANT. Whenever you work on live circuits that use high voltages prepare the measurement setup when everything is off and unplugged from the grid. Then put one hand in the pocket, reconnect power and press "ON". Before doing any adjustment switch off the device under test and unplug the AC cord. If you are unsure, let someone expert do it.
Why didn't I aim for the 1:10 ratio? First and foremost because I needed "now" to measure that voltage. Second because I wanted to use those high value resistors. Third because it's hard (and expensive) to get a perfect 1:10 ratio, so I would have used a calculator anyway: any ratio is good, then! Fourth because I had an excuse to use one of the vintage calculators from my collection.
