SCIENCE · INVESTIGATE AND EXPLAIN

Close node current and loop energy in a mixed network

A circuit diagram specifies which terminals share a node, not where components happen to be drawn on a page. Here a 12 V ideal source feeds one 6 Ω resistor, followed by two branches that reunite at the source return. The branch resistors are parallel because their two endpoint nodes coincide. Their currents need not be equal, but their potential differences must match under the ideal-wire assumption.

Learning outcome: Compare B=10,20,30 Ω at fixed A=20 Ω. Predict the unchanged branch current before checking. Retain the node and power residuals, then redraw the same connections in a different spatial layout without changing the calculations.

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

At A=20 Ω and B=30 Ω, Rp=12 Ω and total current 2/3 A. The node voltage is 8 V; branch currents are .4 and 4/15 A. Source power 8 W splits into 8/3 W in the series element, 3.2 W in the first branch and 32/15 W in the second.

Open the experiment

Predict

Two elements are parallel when:

Your prediction and reason

Experiment

Compare B=10,20,30 Ω at fixed A=20 Ω. Predict the unchanged branch current before checking. Retain the node and power residuals, then redraw the same connections in a different spatial layout without changing the calculations.

Close node current and loop energy in a mixed network

Worked teaching model · synthetic values · Ideal 12 V source feeds a 6 ohm resistor in series with two parallel resistors. Ohmic elements, fixed temperature, ideal wires. Node voltage referenced to source negative. Diagram topology, not physical wiring instructions.

First parallel resistance: 20 Ω Second parallel resistance: 30 Ω

Reset keeps your prediction, captures and practice history.

Node voltage when one branch changes

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

Equivalent numerical coordinates for Node voltage when one branch changes

same topology

second branch resistance (Ω)	node voltage (V)
10	6.31579
10.5	6.41221
11	6.50246
11.5	6.58711
12	6.66667
12.5	6.74157
13	6.81223
13.5	6.87898
14	6.94215
14.5	7.00201
15	7.05882
15.5	7.11281
16	7.16418
16.5	7.21311
17	7.25979
17.5	7.30435
18	7.34694
18.5	7.38769
19	7.42671
19.5	7.46411
20	7.5
20.5	7.53446
21	7.56757
21.5	7.59941
22	7.63006
22.5	7.65957
23	7.68802
23.5	7.71546
24	7.74194
24.5	7.7675
25	7.79221
25.5	7.81609
26	7.8392
26.5	7.86156
27	7.88321
27.5	7.90419
28	7.92453
28.5	7.94425
29	7.96339
29.5	7.98196
30	8

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
Parallel equivalent resistance	12	Ω
Source current	0.666667	A
Common parallel voltage	8	V
First branch current	0.4	A
Second branch current	0.266667	A
Node current residual	-5.55112e-17	A
Source power	8	W
Series resistor power	2.66667	W
First branch power	3.2	W
Second branch power	2.13333	W
Power residual	4.44089e-16	W

Parallel branches share voltage; their currents add at the junction.

Rparallel=R1R2/(R1+R2), not R1+R2. The series element carries total current, while each branch carries Vnode/Rbranch. Kirchhoff node and loop relations reflect charge continuity and energy per charge; their residuals are consistency checks on this model, not independent observations. Changing one branch changes the node voltage and hence the other branch current.

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

Parallel branches share voltage; their currents add at the junction.

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

Equivalent node list: source positive → 6 Ω → N; N → A → return; N → B → return; return → source negative. Moving symbols without changing this node list leaves the ideal network unchanged.

Derive the quantitative response

For branch resistances A and B, 1/Rp=1/A+1/B, or Rp=AB/(A+B). Total source current is I=12/(6+Rp), and the common branch voltage is Vnode=IRp. Branch currents Vnode/A and Vnode/B sum to I. The series resistor carries the total current, not one branch current. Around either closed loop, the source rise equals the two resistor drops. These are charge-continuity and energy-per-charge statements, not rules inferred from the visual length of wires.

Check evidence and the limits of the model

Power offers a second account: source transfer 12I must equal 6I²+Vnode²/A+Vnode²/B. These equalities check arithmetic inside the stated model; they are not independent measured confirmation. Changing one parallel resistance changes Rp, total current and Vnode, so the current in the unchanged branch can change too. A broken branch or an ideal short would require a new topology; do not substitute an arbitrary huge or tiny displayed resistance and silently claim an exact open or short.

Worked original case

Investigation

Changed-case practice

Try the changed case before feedback

Set both parallel branches to 12 Ω while retaining the 6 Ω series resistor and 12 V source. Find source current in A.

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: Infer a source location without assuming an instrument zero Next: Include measuring instruments in the circuit model

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