Explain when a measurement changes the circuit

Establish the model and evidence

An ideal ammeter is placed in series with the current to be measured and has zero resistance. An ideal voltmeter spans the two nodes of interest and has infinite resistance, so it draws no current. These are modeling limits. A real instrument can add resistance or create an additional path, changing the circuit before it reports a value.

The activity begins with a 6 V source and two equal 1 kΩ resistors in series, whose unloaded midpoint is 3 V. A finite voltmeter is then placed across the lower resistor, reducing the effective lower resistance. The measured voltage falls. A nonzero ammeter resistance upstream adds another series drop and can reduce it further. The displayed quantitative correction is supplied enrichment; AP Physics 2 requires qualitative nonideal-meter reasoning.

The upstream ammeter measures total current entering the junction. Some goes through the lower resistor and some through the voltmeter. Dividing the displayed voltage by the lower resistor’s resistance finds only that resistor’s current, not the upstream reading. Matching these two incorrectly can create a false claim that current is not conserved.

Do not use a real ammeter as a voltmeter or connect it directly across a source: its low resistance can produce a dangerous current. The virtual controls never ask you to rewire physical equipment. Supervised meter selection, range checking and safe connection procedures require separate authentic practical instruction; the browser’s idealized network is not a safety certification.

Worked evidence

With a 2 kΩ voltmeter and zero ammeter resistance, the lower equivalent resistance is 666.67 Ω. The reading is 2.4 V, total current 3.6 mA, lower-resistor current 2.4 mA and meter current 1.2 mA. Their sum confirms the junction rule.

Predict and investigate

Will a larger voltmeter resistance make the reading approach or move away from the unloaded 3 V value?

Compare voltmeter resistances 1, 2 and 10 kΩ at zero ammeter resistance. Then add 100 Ω series meter resistance. Explain both disturbances and reconcile the three current entries.

Transfer to changed conditions

A 10 V divider has two equal 2 kΩ resistors. Qualitatively predict the effect of a 2 kΩ voltmeter across the lower resistor; optional numerical enrichment: calculate the reading.

Compare the worked transfer

The reading falls below the unloaded 5 V. The lower pair is 1 kΩ, so the loaded reading is 10×1/(2+1)=3.333 V. This calculation is enrichment, not a practical-meter validation.

Explain the boundary

Why can careful arithmetic fail to recover an unloaded voltage if the model treats the measurement as noninvasive?

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. Original cases and computed/synthetic evidence, not actual laboratory measurements. These activities are virtual only: do not reproduce wiring, short-circuit, battery charging, heating or charged-capacitor experiments. Any real practical work requires qualified supervision and an independently approved safety procedure.