SCIENCE · INVESTIGATE AND EXPLAIN

Track magnetic storage separately from resistor heat

Self-inductance quantifies how a changing current links changing magnetic flux back to the same circuit. In the supplied ideal RL circuit, a6 V source drives a10 Ω resistor and inductance L from zero current. A finite applied voltage cannot create an instantaneous current jump in the ideal inductor. Initially current is zero, resistor voltage is zero and the full source voltage appears across the inductor in passive sign convention.

Learning outcome: Compare t=0, one time constant and a late-time limit. Retain source work, heat and stored energy independently. Then change L at fixed R and predict how half-rise time changes without changing final current.

Starting recap

Use a right-handed coordinate system, oriented surface normal, signed charge/current and declared energy boundary. Separate an entry force from a trajectory, emf from current, and rms from signed average.

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Try

At L=.4 H, τ=.04 s and half-rise time .04ln2≈.027726 s. At one time constant current=.6(1−1/e)≈.379272 A and magnetic energy=.2I²≈.0287695 J. Final stored energy approaches .5(.4)(.6²)=.072 J, while a maintained source continues supplying resistor heat.

Open the experiment

Predict

A self-induced emf opposes:

Your prediction and reason

Experiment

Compare t=0, one time constant and a late-time limit. Retain source work, heat and stored energy independently. Then change L at fixed R and predict how half-rise time changes without changing final current.

Close source, heat and magnetic-energy accounts in an RL rise

Worked teaching model · synthetic values · Ideal series inductor and 10 Ω resistor connected to a 6 V source from zero current. Supplied I=.6[1−exp(−10t/L)] law; no calculus proof required. No mutual coupling, saturation or parasitic capacitance. Switching a real inductor is not requested.

Ideal inductance: 0.4 H Elapsed time: 0.1 s

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Current rise with continuous initial current

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

Equivalent numerical coordinates for Current rise with continuous initial current

supplied RL response

time (s)	current (A)
0	0
0.005	0.0705019
0.01	0.13272
0.015	0.187626
0.02	0.236082
0.025	0.278843
0.03	0.31658
0.035	0.349883
0.04	0.379272
0.045	0.405209
0.05	0.428097
0.055	0.448296
0.06	0.466122
0.065	0.481853
0.07	0.495736
0.075	0.507987
0.08	0.518799
0.085	0.52834
0.09	0.53676
0.095	0.544191
0.1	0.550749
0.105	0.556536
0.11	0.561643
0.115	0.56615
0.12	0.570128
0.125	0.573638
0.13	0.576735
0.135	0.579469
0.14	0.581882
0.145	0.584011
0.15	0.585889
0.155	0.587547
0.16	0.589011
0.165	0.590302
0.17	0.591441
0.175	0.592447
0.18	0.593335
0.185	0.594118
0.19	0.594809
0.195	0.595419
0.2	0.595957

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
Time constant	0.04	s
Current	0.550749	A
Resistor voltage	5.50749	V
Inductor voltage in passive sign convention	0.49251	V
Stored magnetic energy	0.0606649	J
Source work since switch	0.22782	J
Resistor heat since switch	0.167155	J
Energy residual	4.16334e-17	J
Half-rise time	0.0277259	s
Final current limit	0.6	A

The inductor initially takes the source voltage while current starts at zero; stored field energy grows as current rises.

The supplied current law preserves current continuity for a finite applied voltage. Induced emf opposes the change in current, not always the current itself. At long time the ideal inductor voltage approaches zero while current approaches V/R. The accumulated source/heat formulas close Wsource=Qresistor+LI²/2; multiplying endpoint power by time would fail. Half-rise time gives L=R t_half/ln2 only when the effective resistance is independently known.

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

The inductor initially takes the source voltage while current starts at zero; stored field energy grows as current rises.

Observation to attach to a capture

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

Understand

Define vectors, source and system boundary

Derive the quantitative comparison

The supplied algebraic response is I(t)=.6[1−exp(−t/τ)] A with τ=L/10. After one time constant, current reaches about63.2% of its final .6 A; half-rise time is τln2. Knowing half-rise time identifies L only if effective resistance is independently known. An induced emf opposes change in current, not necessarily current itself: during a separately specified decay it would support the previous current direction while energy is released.

Separate physical evidence from a model extension

Magnetic energy is LI²/2. Source work and resistor heat accumulate at changing rates, so neither is found by multiplying the endpoint power by elapsed time. With z=exp(−t/τ), the supplied integrated forms are Wsource=3.6[t−τ(1−z)] and Qheat=3.6[t−2τ(1−z)+τ(1−z²)/2], in joules. Substitution verifies Wsource=Qheat+LI²/2. The model excludes saturation, mutual coupling and parasitic capacitance, and is not an instruction to switch a real inductor.

Worked original case

Investigation

Changed-case practice

Try the changed case before feedback

An ideal RL circuit hasL=.6 H and total resistance15 Ω. Find its time constant in seconds.

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 prose and numerical cases checked 30 October 2026 against the relevant primary explanation. All records and diagrams are virtual. No real coil, powered wire, high-field exposure, motor, transformer, mains connection or inductor switching is requested. Retain first predictions, contrasting recipes and independent criterion review; public agreement is not practical certification or demonstrated mastery.

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

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