SCIENCE · INVESTIGATE AND EXPLAIN

Explain current without consuming charge

Current is the rate at which charge crosses a chosen section: I=ΔQ/Δt, measured in amperes, or coulombs per second. It has a direction convention but is not a spatial vector added by geometric components. Conventional current follows the direction positive charge would move. In a metal the mobile electrons drift in the opposite direction.

Learning outcome: Capture current 0.20 A at areas 0.5, 1.0 and 2.0 mm². Reconcile the identical charge-time slope with changing drift speed. Then increase current alone and explain which graph feature changes.

Starting recap

Distinguish charge flow from energy transfer. Identify nodes, choose consistent current/voltage signs and state source and initial conditions before applying algebra.

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Try

At 0.20 A, 2.0 C passes a section in 10 s, corresponding to about 1.248×10¹⁹ electrons in magnitude. For n=8×10²⁸ m⁻³ and A=1 mm², the supplied formula gives vd≈0.01560 mm/s. The downstream steady current is still 0.20 A.

Open the experiment

Predict

At fixed current, will doubling the area double the transported charge in 10 s, or change the drift speed instead?

Your prediction and reason

Experiment

Capture current 0.20 A at areas 0.5, 1.0 and 2.0 mm². Reconcile the identical charge-time slope with changing drift speed. Then increase current alone and explain which graph feature changes.

Track transported charge and drift without consuming current

Worked teaching model · synthetic values · Uniform hypothetical metallic wire: carrier density 8×10²⁸ m⁻³, electron charge magnitude 1.602176634×10⁻¹⁹ C. Steady current, no accumulation. Electron drift opposes conventional current. Drift calculation is supplied microscopic enrichment, not a signal-propagation speed.

Conventional current: 0.2 A Wire cross section: 1 mm²

Reset keeps your prediction, captures and practice history.

Circuit connections: Closed path with one wire section before and another after a resistive element; both carry the same steady current.

Axes rescale with settings; compare numerical values, not screen angles or apparent lengths. Solid/points show the selected model relationship or observations; the dashed comparison is explained below.

Calculated evidence ledger — synthetic teaching model
Quantity	Value	Unit
Charge passing in 10 s	2	C
Electron count passing in 10 s	12483000000000000000	electrons
Electron drift speed magnitude	0.015604	mm/s
Current at downstream section	0.2	A

Accessible plot coordinates

Primary plotted points
elapsed time (s)	transported conventional charge (C)
0	0
1	0.2
2	0.4
3	0.6
4	0.8
5	1
6	1.2
7	1.4
8	1.6
9	1.8
10	2

The charge–time slope is current; charges transfer energy without being consumed.

Carrier random thermal motion does not imply net current. Electron drift is opposite the chosen conventional current and is not the speed at which an electrical disturbance propagates. Doubling area at fixed current halves drift speed.

The charge–time slope is current; charges transfer energy without being consumed.

Observation to attach to a capture

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

Understand

Establish the model and evidence

A steady series circuit has the same current before and after a resistor. The resistor receives electrical energy and transfers it to other forms; it does not consume electrons. If more charge entered a section than left it over a sustained interval, charge would accumulate and the condition would not be the assumed steady state. At a junction this same account becomes the junction rule.

Charge carriers already occupy the wire. Closing a circuit changes the electric field and produces a small average drift superimposed on random motion. Zero net current does not mean every carrier is motionless. A slow drift speed also does not mean a distant device waits for one electron to travel from the source; the field disturbance and energy transfer are different from the mean carrier motion.

The supplied microscopic comparison uses I=neAvd, where n is carrier number per volume, e the charge magnitude, A the wire area and vd the drift speed magnitude. It illustrates why more available cross section permits the same current with a smaller drift speed. This model holds current fixed and does not simultaneously assume a fixed voltage or unchanged resistance. Its drift calculation is enrichment, while charge-rate conservation is essential.

Worked evidence

Predict and investigate

At fixed current, will doubling the area double the transported charge in 10 s, or change the drift speed instead?

Capture current 0.20 A at areas 0.5, 1.0 and 2.0 mm². Reconcile the identical charge-time slope with changing drift speed. Then increase current alone and explain which graph feature changes.

Transfer to changed conditions

A node receives 0.45 A. One outgoing branch carries 0.18 A. Find the other outgoing current and charge it transports in 20 s.

Compare the worked transfer

The second outgoing current is 0.27 A by charge conservation. It transports 5.4 C in 20 s. The argument assumes no sustained charge accumulation at the node.

Explain the boundary

Explain why a battery supplies energy rather than a one-way stock of electrons that disappears in a resistor.

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. Original cases and computed/synthetic evidence, not actual laboratory measurements. These activities are virtual only: do not reproduce wiring, short-circuit, battery charging, heating or charged-capacitor experiments. Any real practical work requires qualified supervision and an independently approved safety procedure.

Apply

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

Explain why a battery supplies energy rather than a one-way stock of electrons that disappears in a resistor.

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: Reconcile charged-particle deflection with an energy ledger Next: Separate resistance geometry from a power claim

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