Electric Current
▶︎ Watch it animatedinteractive step-through · ~3 min · optional ⚙︎ Open the appletDrift Lab · set the current, the wire and the metal, and read the drift speed against the signal speed on one log scaleCurrent is the rate at which charge crosses a surface, $I = dQ/dt$, drawn in the direction positive carriers would move. Underneath it, $I = nqAv_d$ counts the carriers: density $n$, charge $q$ each, cross-section $A$, and an average drift speed $v_d$ riding on top of fast random thermal motion. Solving for $v_d = I/(nqA)$ gives a quarter of a millimeter per second for a few amps in household copper, while the current density $J = I/A = nqv_d$ describes the same flow per unit area.
Two errors dominate. The first collapses the carrier speed into the circuit's response time, so the lamp is said to light because electrons raced to it, or, having met drift speed, the student cannot explain why anything turns on quickly; the field propagates near $c$ and sets carriers moving everywhere at once, including inside the filament. The second reads $I = nqAv_d$ upside down, expecting a fatter wire to drift faster at fixed current when the product $Av_d$ is what is pinned, forgetting that doubling a radius quadruples the area, or substituting the wire's length for its cross-section.
The work
3 ways in · any order
Lesson
Electric Current
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Builds I = nqAv_d from a cylinder of carriers, drills the scaling that makes a fatter wire drift slower, and settles why a lamp lights in nanoseconds while its electrons take hours to cross the room.
Diagnostic
10-item topic check
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Ten items spanning the failure modes of this topic: conflating drift speed with the speed a circuit responds, expecting a thick wire to drift faster at fixed current, forgetting that the radius enters the area squared, and letting carrier density or wire length wander into the wrong slot. Take it cold to find which one is yours, or after the lesson to confirm it is not.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.