B.5.MPC.R:5.3 - The voltmeter changes the circuit being inferred

An ideal 10 V source drives two 1 MΩ resistors in series. The wanted quantity is the midpoint voltage before a meter is connected. The divider relation gives 5 V.

A voltmeter with 1 MΩ input resistance is connected between the midpoint and the lower terminal. In the connected circuit it lies in parallel with the lower resistor, whose combined resistance becomes 0.5 MΩ. The same divider construction now gives:

V_mid=10*0.5/(1+0.5)=10/3 V.

The indicated value can agree with the connected-circuit model. Comparing it directly with the unloaded prediction had omitted the meter’s interaction.

One repair is inferential: with these resistor, source and meter models, recover the unloaded value from the model, keeping its conditional status. Another is experimental: choose a measurement arrangement whose loading is small enough for the wanted use and account for its remaining effect. Repeating the same connection alone preserves the load.

The result tells the practitioner which voltage was observed and how the wanted voltage can be obtained. A different observed value may require revisiting the assumed source, resistor or instrument behavior through their subject methods.