Bound a diagnosis by its hypotheses and instruments

A unique match still has a boundary

Two readings identify one mechanism among the five supplied cases. That is a useful result, but the scope matters. The hypotheses assume steady ideal sources, fixed resistors, ideal wires and meters, and the listed individual changes. They do not include every combination of damage, calibration error, contact resistance or instrument loading. A unique match means “unique within this stated set,” not “every possible real explanation excluded.”

Review one retained diagnostic notebook case. State the probe definitions, units, predictions, results and compatible mechanisms without using the case letter as your explanation. If you reveal the supplied answer, retain that exposure. The case labels A–E are identifiers for public practice, not concealed examination items. Generic captures cannot replace the dedicated two-reading history.

Test an expanded hypothesis on paper

The healthy nominal circuit has a 6 V source, R1 = 100 Ω and R2 = 200 Ω. It gives 20 mA and junction voltage 4 V. Suppose a different circuit instead has R1 = 300 Ω and R2 = 600 Ω, still driven by an ideal 6 V source. Total resistance becomes 900 Ω, so current is 6/900 A ≈ 6.667 mA. The junction remains (6/900) × 600 = 4 V.

Terminal and junction voltages would therefore look healthy, although both resistor values changed. The resistance ratio stayed the same. Current would distinguish this expanded paper hypothesis from the nominal healthy circuit. This case is not part of the widget’s five supported mechanisms; do not claim it was measured or run through the notebook. It shows why the chosen hypothesis set matters to a diagnosis.

An outcome matching none of the five candidates is also meaningful. It could indicate an incomplete model, inconsistent units or polarity, a transcription problem, or behavior outside the ideal assumptions. Do not force the nearest listed fault without a justified error model. The exact synthetic readings provide no numerical tolerance distribution or likelihoods for unlisted values.

Instruments can change what they measure

The virtual voltmeter has infinite resistance and draws no current. A real voltage measurement can instead create an additional conducting path. As a deliberately exaggerated paper example, place a hypothetical 200 Ω voltmeter across the healthy 200 Ω R2. Their parallel combination is 100 Ω. With R1 still 100 Ω and source 6 V, total current becomes 30 mA and the junction becomes 3 V. The meter would have changed the divider it was meant to inspect.

This is a calculation about a hypothetical meter, not a typical instrument specification or another selectable fault. OpenStax’s measuring-instrument discussion explains instrument resistance and its effects. An ammeter with nonzero resistance can likewise change a series current; the present notebook deliberately omits these effects.

Distinguish an additional check from a rewritten history

If you suspect meter offset, propose checking a known reference with stated uncertainty and the same range. If you suspect loading, request the instrument’s input-resistance specification and analyze the connection. A reference check does not automatically rule out topology faults, and knowing input resistance does not establish every calibration property.

Keep these proposed checks separate from the two already obtained readings. A two-probe budget can leave a justified unresolved conclusion. A later expanded investigation needs a new evidence record; it must not silently replace original predictions or pretend a revealed public answer was an independent observation. Repeating the same deterministic case supplies no new sample of real device reliability.

Transfer: a supplied additive offset

On paper, an ideal healthy circuit’s actual terminal and junction differences are 6 V and 4 V. A hypothetical voltmeter adds a known +0.5 V to each indicated reading. Predict the two indications, apply the correction and state one limitation that remains. The current reading comes from a separate ideal ammeter and is unchanged.

Check the offset-and-scope transfer

The indications are 6.5 V and 4.5 V. Subtracting the supplied offset gives 6 V and 4 V; the current remains 20 mA. This corrects the stipulated additive error only. It does not prove that an actual meter has that offset, eliminate loading or establish that the correction applies at other values. These hypothetical indications are separate paper evidence, not altered case receipts.

Conclude with one bounded claim and one discriminating follow-up. Return to calibration comparison or measurement budgeting if either part is weak. Independent diagnosis requires a genuinely unfamiliar assignment, disclosed help and human review of the reasoning; successfully recalling these public cases does not establish it.