AS 91526 · 2025 paper · inductors

Question 2(c) Merit to Excellence

Mereana connects an old coil to her caravan battery. The coil is modelled as a 0.600 H inductor in series with a 2.40 Ω resistor; the 12.6 V battery has an internal resistance of 0.100 Ω.

L	0.600 H
R(coil)	2.40 Ω
ε	12.6 V
r	0.100 Ω

When the switch is opened, a small spark is seen where it breaks the circuit.

Explain why the spark is produced.

The 2025 paper, page 5 ↗ Marking schedule, page 4 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1 When the switch opens, what happens to the current and to the magnetic field in the coil?
The current drops towards zero, so the magnetic field (the flux through the coil) collapses.
2 What does a changing current do in an inductor?
It induces an EMF that opposes the change, ε = −L ΔI/Δt. Here it acts to keep the current flowing.
3 Why is the change so fast? Think about what the open switch adds to the circuit.
The gap in the switch is air, which is a huge resistance. τ = L / R becomes tiny, so the current collapses in a very short Δt.
4 Put the two together.
A large ΔI over a tiny Δt makes ε = −L ΔI/Δt very large. That voltage across the small gap is enough to ionise the air, and current jumps across it as a spark.

Answer Opening the switch collapses the current and the flux very quickly, because the air gap’s huge resistance makes τ = L / R tiny. A fast change induces a large EMF, ε = −L ΔI/Δt, which ionises the air across the gap: that is the spark.

What the marker wanted

Achieved One idea: an EMF is induced, the current drops suddenly, the field collapses, the time constant gets smaller, or the resistance becomes large.
Merit Gives the reason an EMF appears across the coil, or the reason the current collapses so fast (τ = L / R).
Excellence Gives both reasons: where the EMF comes from, and why Δt is so short (the huge resistance of the gap), or uses Kirchhoff’s loop law to explain why the whole large EMF appears across the gap.

In our words, from NZQA’s 2025 marking schedule.

Common mistake

Stopping at “a back EMF is induced”. That names the effect, which is Achieved. Merit needs the reason, and Excellence also needs why the change is so fast.

How did it go?

Got it moves it further out. Review brings it back tomorrow.