Electric Current
Distinguish conventional current from carrier drift and use current-time area and charge-time slope.
AP Physics 2 Topic 11.1 · College Board CED printed p. 61 / PDF p. 68 · See this topic in the course outline
Current counts charge crossing a surface each second. The charges are already in the wires; a battery supplies an energy difference that supports their organized motion.
For a supporting original reading, see Current and Resistance. Follow charge-flow rate and conventional-current direction; keep electron drift opposite the arrows.
Before you start
- Charge conservation and elementary charge
- Potential difference and electric force
Current measures net charge flow
The average current through a wire cross section is , in amperes (1 A = 1 C/s). Here Δq is the net charge flow counted with a specified direction. A larger current can mean more carriers crossing per second or a larger charge per carrier. For electrons, the magnitude of the carrier count is .
A maintained potential difference establishes an electric field that drives charge motion through the circuit. A source’s emf ε is its supplied energy per charge, measured in volts; it is not a mechanical force in newtons. Even when I = 0, charge carriers still have random microscopic motion. Zero current means no net directed carrier flow through the cross section, not that every electron is motionless.
Conventional current and electron drift
Conventional current points in the direction positive charge would move. In ordinary metallic wires, the carriers are electrons, so their average drift is opposite conventional current. Through an external resistor, conventional current points from the higher-potential end to the lower-potential end; negative carriers drift the other way.
Current has a direction attached to the path of a circuit branch, but it is not a spatial vector to add by x and y components. A wire can bend through 90° while carrying the same current everywhere along an unbranched path. At a junction, add signed rates of charge flow; do not multiply them by the angles between wires. You may assume a branch direction and solve for I; a negative result means flow opposite that arrow.
Charge crossing a bent wire
A constant conventional current of 0.40 A flows clockwise through an unbranched metallic loop for 15 s. Find net charge flow and the number and drift direction of electrons at one wire cross section.
|Δq| = IΔt = (0.40)(15) = 6.0 C.
Why this step? Current is charge crossing per time, independent of the wire’s bend.
N = 6.0/(1.60 × 10⁻¹⁹) = 3.75 × 10¹⁹ electrons.
Why this step? Each electron has charge magnitude e.
The electrons drift counterclockwise, opposite the clockwise conventional-current arrow.
Why this step? The carrier charge is negative.
Answer and check
6.0 C of net charge-flow magnitude; about 3.8 × 10¹⁹ electrons drift counterclockwise.
Voltage organizes motion that already exists
Mobile electrons already exist in a metal, even before a circuit is closed. Random microscopic motion can give zero net crossing of a wire’s cross section. A maintained potential difference supports an electric field inside a resistive wire. The field exerts forces on carriers and produces an average drift, giving nonzero net charge flow. Electrons drift opposite the field and conventional current points in the positive-charge direction.
Current is the rate of net charge crossing a section, I = Δq/Δt. It is not the speed of one electron and is not a spatial vector whose magnitude loses a cosine factor at a bend. The battery supplies energy per charge; it does not create the circuit’s carriers. For steady unbranched current, the same rate passes every section, including a bend.
Switching from random motion to a net flow
A 10 Ω fixed-temperature resistive loop is connected to an ideal 2.0 V battery. Before closing, current is zero. After steady current is established, consider a 5.0 s interval.
- Before closing, electrons need not be motionless: their random crossing contributions have zero net directed flow.
- After closing, a maintained voltage supports a field and electron drift. I = 2.0/10 = 0.20 A in the conventional external high-to-low-potential direction; electrons drift oppositely.
- Net flow magnitude is IΔt = 1.0 C, corresponding to 1.0/(1.60 × 10⁻¹⁹) = 6.25 × 10¹⁸ net electron crossings. Individual random recrossings are not counted by this net number.
- The battery supplies 2.0 J per coulomb and therefore 2.0 J during this interval, converted thermally in the fixed-R loop.
Answer and check
0.20 A, 1.0 C net flow and 6.25 × 10¹⁸ net electron crossings in 5.0 s; carriers were present before closing.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
A metal wire has zero current. Must the electrons be at rest? What changes when a potential difference is maintained?
Worked answer and reason
No. Random electron motion can continue with zero net flow. A maintained potential difference establishes an electric field and supports a nonzero average drift and current.
Current measures net directed flow, while microscopic motion can cancel in the average.
Question 2
A wire turns a corner without branching. Does current fall by a factor cos90°? Which way do electrons drift relative to its current arrow?
Worked answer and reason
No; the same charge rate crosses each section of an unbranched steady path. Electrons drift opposite the arrow.
Current is a branch charge-flow rate rather than a spatial vector.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- The battery sends newly created electrons through a bulb.
- Mobile charges already occupy the conducting circuit; the source transfers energy and maintains a potential difference.
- No current means no electron motion.
- It means no net organized charge flow, while random motion remains.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
- Problem 1 · current-time area and carrier count
- Problem 2 · comparison and energy-per-charge explanation
- Problem 17 · resistance experiment, uncertainty, and power
Explain and apply the model
Try these problems before opening the solutions. Show the physical model, your calculation or sketch, and the reason your conclusion follows.
What starts the net current?
A metal resistor is connected into a closed loop with a maintained battery potential difference. Its temperature and resistance are approximately fixed.
(a) Which explanation connects the source to charge motion correctly?
Worked solution and rubric →Revisit the explanation →Revisit the explanation →
Scientific calculator workspace
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Scientific calculator
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For the teacher
- Have students distinguish a charge-flow rate from carrier drift speed.
- Ask students to redraw electron arrows without changing the conventional-current schematic.
Source objectives and scope
- 11.1.A — Describe the movement of electric charges through a medium.
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- College Board AP Physics 2 Course and Exam Description, Unit 11 (PDF pages 68–81) — Official topic order, learning objectives, all essential-knowledge clauses and boundaries. Equation pages 68,71,73,75,77–80 and relevant continuation pages visually inspected; independent reviewed-source-equation overlay consulted.
- OpenStax University Physics Volume 2, 9.3 Resistivity and Resistance — Independent verification of real material temperature dependence and the fixed-temperature qualification for linear metallic response. Teaching and assessment prose are original.
- OpenStax University Physics Volume 2, 10.3 Kirchhoff’s Rules — Independent verification of conservation-based branch and loop analysis; no calculus is needed in these authored tasks.
- Corrected original reading: Current and Resistance — Follow charge-flow rate and conventional-current direction; keep electron drift opposite the arrows.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: Introduction to Circuits — Practice node connectivity, switches and common symbols. Check that any short-circuit idealization retains a finite current-limiting resistance.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: Resistors in Circuits — Connect resistor voltage and current to energy transfer per second. Brightness comparisons require a stated bulb model.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: Kirchhoff’s Laws — Trace actual closed paths and keep signed voltage changes. Use independent equations rather than combining disconnected branches into one loop.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: Capacitors in Circuits — Compare equal-charge series and equal-voltage parallel capacitor arrangements.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: RC Circuits — Use initial and long-time states, τ and qualitative curves. Source exponential and logarithmic transient calculations extend beyond required AP Physics 2 modeling.Supporting context; original AP teaching and practice above remain independently authored.
Glossary and deeper reading · 14 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Electric charge
Electric charge is a conserved property that determines electric interactions. It can be positive or negative and is measured in coulombs; ordinary net charges arise from an imbalance of charged particles. For example, transferring electrons between initially neutral objects leaves one negatively charged and the other positively charged.
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Drift velocity
Drift velocity is the small average carrier velocity associated with net charge flow in a conductor. It is distinct from the carriers’ random microscopic motion and from the speed at which a circuit’s electromagnetic changes propagate. For example, electrons can drift slowly along a wire while a circuit responds rapidly when a switch closes.
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Elementary charge
The elementary charge is the magnitude of the charge carried by a proton or electron, approximately 1.60 × 10⁻¹⁹ coulomb. A proton carries positive elementary charge and an electron carries negative elementary charge. For example, removing one electron from a neutral atom leaves it with a net charge of one positive elementary charge.
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Potential difference
Potential difference is the change in electric potential between two locations. It represents electric potential-energy change per unit charge and is measured in volts. For example, the potential difference across a resistor describes the energy transferred per coulomb passing through it.
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Electric force
Electric force is the interaction of an electric field with a charged object. For point charges at rest, like signs repel and opposite signs attract, with direction along their separation. For example, an electron and proton exert equal-magnitude opposite forces on one another despite having different masses.
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Electric field
An electric field assigns the electric force per unit positive test charge to each location. The field is produced by the sources and is a vector, while the force on a negative charge points opposite the field. For example, the electric field between ideal parallel capacitor plates can accelerate an electron opposite the field arrows.
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Electromotive force
Electromotive force is energy supplied per unit charge by a source or induction process. Despite its name it is measured in volts, rather than newtons, and can exist even when no current flows. For example, an ideal battery supplies an emf while an induced emf can be produced by changing magnetic flux.
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Conventional current
Conventional current points in the direction that positive charge would move through a circuit. In a metal wire, electrons usually drift in the opposite direction. For example, a current arrow pointing right in a metal wire does not mean the conduction electrons drift right.
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Vector
A vector is a quantity with a magnitude and a direction, represented by an arrow or by components along chosen axes. Vectors add by adding corresponding components rather than simply adding their magnitudes. For example, an eastward displacement followed by a northward displacement produces a resultant pointing northeast. The zero vector has zero magnitude and no unique direction.
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Circuit node
A circuit node is a connected conducting region treated as having one potential in the ideal-wire model. Branches meet at nodes, so topology rather than the drawing’s shape determines how elements are connected. For example, moving a wire on a schematic without changing its connections leaves the circuit nodes unchanged.
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Force
A force describes an interaction that can change an object’s momentum. It is a vector measured in newtons, so both size and direction matter when forces are added. For example, a rope can pull a cart while the floor exerts friction in another direction.
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Magnitude
Magnitude is the nonnegative size of a vector quantity. It does not specify direction, and it differs from a signed component. For example, a westward velocity can have a negative x component while its speed, the velocity magnitude, stays positive.
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Temperature
Temperature is a state quantity that determines the direction of net energy transfer through thermal contact. For a classical ideal gas it is proportional to the average translational kinetic energy per particle, rather than to the total energy of the sample. For example, a small hot metal sample can have a higher temperature but less total internal energy than a large cooler sample.
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Electrical resistance
Electrical resistance relates the potential difference across an element to the current through it. It is measured in ohms and depends on the element’s material, geometry, and conditions. For example, a longer uniform wire has greater resistance when cross-sectional area and material remain fixed.