= Voltage divider teaching experiment
Southern Illinois University's ET 304A guide, \i[Lab 4: Voltage Measurements and Meter Loading Effects], documents an instructive test: build equal-arm <voltage dividers> on a $20\,\mathrm V$ supply, then measure across the lower arm with a digital <multimeter>, analog <multimeter>, and <oscilloscope>. Starting with two $10\,\mathrm{k\Omega}$ <resistors>, repeat with equal pairs from $220\,\mathrm{k\Omega}$ to $4.7\,\mathrm{M\Omega}$. It requires separate recorded readings, unloaded predictions, and predictions including each instrument's input <electrical resistance>. The guide obtains meter resistances from specification sheets and scope resistance from the input-panel marking. Equal ratios control the unloaded target while changing susceptibility to <voltmeter loading>. The provided tables are blank: the guide specifies a procedure, not measured outcomes.<Lab 4: Voltage Measurements and Meter Loading Effects, Southern Illinois University ET 304A>[pp. 2–3, Figure 2, Procedure steps 1–13 and report requirements; pp. 4–5, blank tables]{ref}
Preparation and accuracy checks are made concrete by Berkeley's \i[Lab 1: Introductory Experiments and Linear Circuits I]. Its different divider uses nominal $470\,\mathrm{k\Omega}$ and $10\,\mathrm{k\Omega}$ <resistors> and a $24\,\mathrm V$ supply on a breadboard. Measure isolated <resistors> first, record actual supply voltage, recalculate with these measured values, then record the junction voltage with the digital <multimeter>. It explicitly compares actual values with <resistor tolerance> and the final voltage with a range-dependent accuracy bound from the instrument manual. This is an uncertainty check, not an independent <measurement calibration>.<Lab 1: Introductory Experiments and Linear Circuits I, UC Berkeley Physics 111A>[Resistance instructions; Problems 1.1.8–1.1.10: component/supply preparation, recalculation and readout accuracy]{ref}
For a controlled comparison, additionally record the selected instrument range, probe factor, and input coupling; connect each instrument separately to the same <electrical reference potential>, and monitor the input rather than treating the supply label as an exact voltage. These are proposed controls for interpreting the documented procedures. A voltage indication and a resistance indication from the same digital <multimeter> do not independently validate its <measurement calibration>; a traceable reference comparison would be needed for that. <Resistor tolerance> describes component variation, while <measurement uncertainty> describes what is known about measured values. Using nominal arms alone can confuse mismatch with loading: equal nominal arms each within one-percent tolerance can give unloaded ratios from $0.495$ to $0.505$.
The inference to test is specific: once actual arm values, input voltage, and meter input <electrical resistance> are accounted for, the readout should approach the <loaded voltage divider> prediction within the remaining <measurement uncertainty>. A discrepancy can instead reflect contacts, changing <temperature>, source droop, or an input that is not a fixed passive <resistor>. A source with positive series <electrical resistance> $R_s$ can be modeled by replacing $R_1$ with $R_1+R_s$ only when $V_s$ denotes its ideal internal voltage; when the actual voltage across the divider is measured, that terminal value is already $V_{\mathrm{in}}$. During settling, or with appreciable input <capacitance> and changing <signals>, the steady <direct current> calculation is insufficient. Neither institutional procedure supplies measured values for the original $10\,\mathrm V$ example above.
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