The trace is a teaching model, not a recording. The arc lights once the gap sees 50 V and burns at about 30 V. The fuzz is drawn much larger than life.
This model AFCI trips after 8 arcing half cycles in half a second. Real AFCIs use their makers' own methods and are tested to UL 1699. Trip times here are the model's.
Many AFCIs also shut off on current leaking to ground. This model leaves that out.
Both breakers have a bimetal that heats with current. The magnetic trip, which a solid short would set off, is not drawn.
Heat at the arc is the arc's volts times its amps. The glow shows where the heat is. Browning is sped up.
The nail touches through 1.6 Ω of charred insulation and sparks on and off, so bursts reach about 80 A. A solid short draws far more.
40 ft of 12 AWG NM on a 20 A breaker and 6 ft of 16 AWG cord, Chapter 9 Table 8.
A 1500 W heater is rated 12.5 A, more than 80% of a 15 A circuit, so it gets a 20 A circuit, 210.23(B)(1).
Article 100 defines the AFCI. New bedroom circuits need one, 210.12(B); a combination AFCI breaker is one way, 210.12(A)(1). Older homes need one when a bedroom circuit is changed, 210.12(E).
A bored hole's edge must be at least 1-1/4 in. from the stud face, or the cable needs a steel plate, 300.6(A)(1).
Splices go in boxes you can get to, 314.29. Never bury one in the wall.
Receptacles in a home must be tamper-resistant, 406.26. This one is a 20 A receptacle.
The neutral-to-ground bond is at the service and isn't drawn.
Speeds are fractions of real time. Slow it down to see each half cycle.