Make a prediction that a measurement could reject
The browser calculates ideal circuit values. Matching its two tables to each other checks a model, not a physical apparatus. This investigation asks whether readings support a nominal 100 Ω and 200 Ω series pair, and what evidence distinguishes circuit faults.
Choose either instructor-supervised physical measurements or the original synthetic practice data below. Label the choice in your report. Synthetic data are invented readings for analysis practice; they are not observations you made. The notebook saves text and model settings, but does not parse your measurements or certify wiring skill. Keep a separate raw-data sheet if needed.
Before collecting or opening the readings, set R2 = 200 Ω and capture source voltages 2, 6 and 10 V. Predict series currents of approximately 6.667, 20.000 and 33.333 mA. Draw a closed loop and mark the two points across which you would measure source terminal voltage.
Plan the instruments and the physical scope
A voltmeter connects across the two points whose potential difference is wanted. An ammeter is inserted in the path whose current is wanted. In a series loop, it carries the same current as the resistors; connecting a current-mode meter directly across the source instead creates a low-resistance path. Resistance measurement uses an isolated, unpowered component.
For the optional physical series experiment, use an instructor-approved current-limited DC supply, nominal 100 Ω and 200 Ω resistors rated at least 1 W, suitable leads, and meters with known ranges and specifications. Limit this procedure to 2–10 V and an instructor-set 50 mA current limit. The nominal series current stays below 34 mA, and the larger resistor’s predicted dissipation stays below 0.223 W. Do not translate the browser’s higher-power parallel settings into this apparatus procedure. Disconnect power before changing wiring or meter mode, and have the instructor verify connections, terminals and range. Record any current-limit indication; it changes the assumed source behavior.
OpenStax: electrical measuring instruments explains meter placement and instrument resistance. The procedure, numerical datasets and diagnostic cases here are original activities.
Collect evidence with a reproducible record
- Record resistor labels, tolerances, meter models, range, display resolution and the accuracy specification for that range. A display’s last digit is not automatically the measurement’s accuracy. Sketch every meter connection and record the chosen polarity.
- With the source off, build the series loop and insert the current meter. Put the voltage meter across the source terminals. Verify the arrangement before energizing it.
- At nominal settings 2, 4, 6, 8 and 10 V, record measured terminal voltage and current, including units and signs. Do not substitute the dial setting for a measurement. Allow stable readings and note drift or a current-limit indicator.
- At nominal 6 V, take five readings over the same stated interval without changing the connections. Record all readings. These assess short-term repeatability, not five independent resistor specimens or five independent calibrations.
- Return to an earlier voltage to look for drift or heating effects. Record the result even if it disagrees with the first pass. Disconnect power before inspecting or changing connections.
- Compare your predictions with observations. Retain discrepant rows and explain exclusions. If one meter is reused, document the power-off rewiring and the fact that readings were sequential; do not describe them as simultaneous.
Analyze the supplied alternative
These values were invented to lie near, but not exactly on, a 300 Ω series model. The current readings include small deviations deliberately; the number of digits is part of this exercise, not a claim about a real meter.
| Nominal setting (V) | Terminal reading (V) | Current reading (mA) |
|---|
| 2 | 2.00 | 6.7 |
| 4 | 4.01 | 13.2 |
| 6 | 5.99 | 20.1 |
| 8 | 8.00 | 26.5 |
| 10 | 10.02 | 33.4 |
A separate five-reading sequence at nominal 6 V is 20.0, 20.1, 19.9, 20.0, 20.1 mA. Its mean is 20.02 mA and its range is 0.2 mA. This repeatability summary does not establish that the meter’s offset is zero. A common calibration error can persist through every repetition. Treat this sequence separately from the sweep row, not as six repeated readings collected under a documented identical procedure.
Estimate a resistance before checking the middle rows
Use the two endpoint rows to estimate the slope of voltage versus current:
R estimate = (V high − V low)/(I high − I low).
Convert milliamperes to amperes before dividing. Here ΔV = 8.02 V and ΔI = 0.0267 A, giving R estimate ≈ 300.375 Ω. The line through these endpoints is V ≈ (300.375 Ω)I − 0.01251 V. This is a two-point estimate, not a least-squares fit. Its small intercept is not by itself evidence of a real meter offset.
Keep the three interior rows out of the estimate, then check whether they agree with its predictions. At terminal voltage 5.99 V, the line predicts approximately 19.983 mA; the observed 20.1 mA differs by +0.117 mA. Also compare the nominal 300 Ω prediction, 5.99/300 ≈ 19.967 mA. An endpoint-derived model and a nominal-component model are different claims. If you revise the model using the interior readings, those readings become development evidence; obtain new data for a fresh check.
Check all interior current residuals
The endpoint line predicts approximately 13.392 mA at 4.01 V, 19.983 mA at 5.99 V and 26.675 mA at 8.00 V. Observed-minus-predicted residuals are approximately −0.192, +0.117 and −0.175 mA. These small residuals alone do not establish that a real resistor stays ohmic over other voltages, temperatures or durations.
State an uncertainty model rather than inventing precision
For this synthetic exercise, stipulate bounds of ±0.02 V per voltage reading and ±0.2 mA per current reading. They are assumed worst-case bounds, not confidence intervals inferred from the five repetitions. In physical work, replace them with justified instrument and procedure information.
Allowing endpoint errors to vary independently within those bounds gives ΔV between 7.98 and 8.06 V, and ΔI between 0.0263 and 0.0271 A. Because both differences are positive, an enclosing slope interval is:
7.98/0.0271 ≤ R estimate ≤ 8.06/0.0263, or approximately 294.5–306.5 Ω.
The nominal 300 Ω lies inside that interval. Report compatibility with the stated assumptions, not proof of exact resistance. If errors share a fixed offset, that offset cancels in differences; a gain error need not cancel. The independent worst-case model is a conservative choice for this exercise, not a universal description of correlated meter errors. The interval also does not include every possible source of model error, such as changing resistance with temperature.
The measuring instrument can change the circuit
The browser assumes ideal instrumentation. As a separate calculation, insert an ammeter with 10 Ω resistance into the 6 V, 300 Ω series loop. Current becomes 6/310 ≈ 19.355 mA, about 3.23% below the ideal 20 mA. That difference is a modeled loading effect, not random scatter that averaging removes. Ten ohms is an illustrative assumption, not a specification for the physical meter.
A finite-resistance voltmeter similarly creates an additional branch across the part it measures. Predict whether that could alter a divider voltage before measuring it. Use the actual instrument’s specifications when judging whether loading is negligible. Neither effect is simulated by the existing browser controls.
Diagnose competing explanations with more than one reading
For the following synthetic fault cases, the intended circuit is the parallel 100 Ω and 200 Ω pair. The nominal source setting is 6 V. Table entries are terminal voltage, branch currents and total current; treat values as exact within this diagnostic exercise, separately from the uncertainty exercise above.
| Case | Terminal V | Currents R1 / R2 / total (mA) |
|---|
| A | 6.0 | 60 / 0 / 60 |
| B | 4.8 | 48 / 24 / 72 |
| C | 6.0 | 60 / 60 / 120 |
For each case, name a supported electrical conclusion, at least one alternative cause, and an observation that would distinguish causes. The ideal browser can provide the intended baseline; it cannot reproduce an open branch or source sag merely by changing its finite-resistance presets.
Check the circuit diagnoses
A indicates a nonconducting R2 branch or a problem with its current measurement. It does not identify a failed resistor rather than a broken lead, connection or meter setup. With power disconnected, an instructor can inspect the path and test the isolated component. B is consistent with the intended resistances at a reduced terminal voltage; the readings alone do not distinguish a source setting error, current limiting or internal voltage drop. Check the source indication and compare unloaded and loaded terminal voltage under a documented procedure. C has an effective R2 branch resistance of 6/0.060 = 100 Ω. A wrong resistor or an extra parallel path could produce this, while an incorrect current reading remains another possibility. Inspect the topology and measure the isolated component with power off. Current totals in every row equal the branch sums; that agreement alone does not identify the fault.
Transfer and report
An unfamiliar intended parallel pair has 100 Ω and 300 Ω across 6 V. Before using the browser, predict branch currents and total power. Then select R2 = 300 Ω to check your prediction. Explain which further observation would be needed if total current alone were 80 mA: that total cannot uniquely identify both branch resistances.
Check the new-circuit prediction
Branch currents are 60 and 20 mA; source current is 80 mA. Total power is 6 × 0.080 = 0.480 W. Two other branch resistances could give the same equivalent resistance and source current, so measure branch current or an isolated resistance to distinguish them.
Your report should include a labeled circuit sketch, data provenance, raw readings and meter details, one captured model prediction, the resistance estimate with units and assumptions, a residual on an unused reading, a diagnosis with a discriminating follow-up, and a limitation. A satisfactory numerical match is evidence about the tested conditions; it is not proof of every possible circuit behavior. Notebook completion checks the presence of an explanation, not its quality or independent laboratory proficiency.
