SCIENCE · INVESTIGATE AND EXPLAIN

Include measuring instruments in the circuit model

An ideal voltmeter draws no current, but a real finite input resistance is another parallel branch. An ideal ammeter adds no voltage drop, but a finite burden resistance changes the series path. This virtual packet makes both deviations explicit rather than calling a meter reading the untouched original quantity.

Learning outcome: Compare Rv=10,30,50 kΩ at zero burden, then hold Rv fixed and increase burden. Retain the original lower-resistor current separately from total current. Identify which ideal limit removes each disturbance.

Starting recap

Use charge continuity, energy per charge, consistent SI units and an explicit circuit topology. Exponential responses are supplied algebraic models; initial state, source constraint and measurement loading must be declared.

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Try

With Rv=30 kΩ and zero ammeter burden, L=30000/11 Ω. Total current is 33/13000 A≈2.53846 mA and the indicated lower voltage is 90/13≈6.92308 V, below 7.2 V. A finite series burden reduces it further.

Open the experiment

Predict

The current measured upstream of both the lower resistor and voltmeter equals:

Your prediction and reason

Experiment

Compare Rv=10,30,50 kΩ at zero burden, then hold Rv fixed and increase burden. Retain the original lower-resistor current separately from total current. Identify which ideal limit removes each disturbance.

Include both meters in the measured network

Worked teaching model · synthetic values · Ideal 12 V source, upper resistor 2000 ohm and lower 3000 ohm. Voltmeter is parallel to lower resistor; ammeter burden is in series with the whole divider. Both are supplied linear resistance models. No actual meter connections.

Voltmeter input resistance: 20 kΩ Series ammeter burden resistance: 200 Ω

Reset keeps your prediction, captures and practice history.

Voltmeter loading with fixed ammeter burden

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: finite-input network (solid). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Voltmeter loading with fixed ammeter burden

finite-input network

input resistance (kΩ)	voltage indication (V)
10	6.14334
11	6.2069
12	6.26087
13	6.30728
14	6.34761
15	6.38298
16	6.41425
17	6.44211
18	6.46707
19	6.48956
20	6.50995
21	6.5285
22	6.54545
23	6.56101
24	6.57534
25	6.58858
26	6.60085
27	6.61224
28	6.62286
29	6.63278
30	6.64207
31	6.65077
32	6.65896
33	6.66667
34	6.67394
35	6.68081
36	6.68731
37	6.69347
38	6.69931
39	6.70487
40	6.71016
41	6.7152
42	6.72
43	6.72459
44	6.72897
45	6.73317
46	6.73718
47	6.74104
48	6.74473
49	6.74828
50	6.75169

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

Calculated quantities under the declared measurement model
Quantity	Value	Unit
Uninstrumented divider voltage	7.2	V
Loaded lower equivalent resistance	2608.7	Ω
Ammeter current indication	0.00249548	A
Voltmeter voltage indication	6.50995	V
Original lower resistor current	0.00216998	A
Voltmeter current	0.000325497	A
Ammeter burden voltage	0.499096	V
Voltage measurement change	-0.690054	V

The meter reads the network it helps create, not an untouched ideal divider.

A voltmeter is a parallel branch; an ammeter burden adds series resistance. Infinite input resistance and zero burden are separate ideal limits. The source current includes voltmeter current, so it is not identical to the original lower-resistor current. Correcting a loading effect requires an explicit circuit model and independent meter specifications, not merely more digits.

Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.

The meter reads the network it helps create, not an untouched ideal divider.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Define topology, recipient and initial conditions

Derive the quantitative response

The uninstrumented divider has 2000 Ω above and 3000 Ω below a 12 V source, so its lower voltage is 12×3000/5000=7.2 V. A voltmeter resistance Rv across the lower resistor replaces that lower branch by L=3000Rv/(3000+Rv). A series ammeter burden Ra then gives total current 12/(2000+Ra+L) and indicated lower voltage IL. The ammeter current includes both lower-resistor and voltmeter currents; it does not equal the original lower-branch current by definition.

Check evidence and the limits of the model

Increasing input resistance reduces one loading effect, while reducing ammeter burden addresses another. Neither change removes source drift, resistor tolerance or calibration uncertainty. An exact correction based on assumed meter resistances is still conditional on those specifications. The diagram is a theoretical connectivity task only: no connection to a real battery, outlet, charged capacitor or unknown circuit is requested, and the numerical values are not equipment-selection guidance.

Worked original case

Investigation

Changed-case practice

Try the changed case before feedback

For the stated 2 kΩ/3 kΩ divider, let voltmeter resistance be 3 kΩ and ammeter burden zero. Find indicated lower voltage in V.

Numerical result in the requested units

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and evidence boundary

Original numerical cases and prose checked 30 October 2026 against the relevant primary explanation. All records are synthetic and all diagrams mathematical. No practical wiring, battery testing, capacitor handling, mains measurement or equipment safety rating is requested. Public feedback does not verify independent mastery; retain first predictions, contrasting recipes and criterion-based critique in the separate course evidence workspace.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Which independent observation could reject this model rather than merely refit its parameters?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Close node current and loop energy in a mixed network Next: Compare maximum load power with efficient transfer

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