AS 91526 · 2023 paper · capacitors

Question 1(d) Merit to Excellence

Kate investigates a capacitor found in a camera, labelled 185 nF (1.85 × 10⁻⁷ F). The camera also contains a 1.50 V “AA” battery.

C	185 nF
V	1.50 V

Charged from the 1.5 V battery the bulb barely glows. Kate finds wiring that lets the capacitor be charged to 200 V instead.

Explain how this gives a much more powerful flash — comparing the stored energy, the initial current, and the brightness.

The 2023 paper, page 4 ↗ Marking schedule, page 2 ↗

Work it out

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

1 How does the stored energy depend on the charging voltage?
E = ½CV² with C fixed, so the energy goes as V². At 200 V, E = ½ × 1.85 × 10⁻⁷ × 200² = 3.70 × 10⁻³ J, against 2.08 × 10⁻⁷ J at 1.50 V.
2 How many times more is that?
(200 / 1.50)² = 133² ≈ 1.78 × 10⁴: nearly 18 000 times the energy, from a voltage only 133 times bigger.
3 The moment the switch closes, what sets the current through the bulb?
The capacitor’s voltage across the bulb’s resistance: I₀ = V / R. Same bulb, so the starting current is 133 times bigger. Put another way, 133 times as much charge leaves the plates each second.
4 What decides how bright the flash is?
The power, P = VI: how fast the energy is turned into light and heat. V and I are both 133 times bigger, so the power at the start is about 18 000 times bigger.
5 Does the extra energy take longer to come out?
No. Taking the lamp’s resistance as fixed, the time constant RC is unchanged, so about 18 000 times the energy comes out in roughly the same short time. That is the much brighter flash.

Answer At 200 V the capacitor stores (200/1.5)² ≈ 18 000 times the energy (3.70 × 10⁻³ J). The starting current, I = V/R, is 133 times bigger, so the power, P = VI, is about 18 000 times bigger; with the lamp’s resistance taken as fixed, RC is unchanged, so all that energy comes out in the same short time, as a far brighter flash.

What the marker wanted

Achieved One of: the energy at 200 V, 3.7 × 10⁻³ J; a comparison of the two energies; a bigger current because of more charge, energy or voltage; or a brighter flash because of more voltage, current, power, energy or charge.
Merit Two of: the two energies compared by calculation (133² ≈ 18 000 times); why the current is bigger (more charge flows off the plates each second, or a bigger V drives a bigger I); why the power is bigger (both V and I are larger, so more energy each second).
Excellence All three.

In our words, from NZQA’s 2023 marking schedule.

Common mistake

Stopping at “more energy is stored, so the flash is brighter”. That is an Achieved point. The Merit and Excellence columns also want why the current is bigger and why the power is bigger, and NZQA’s 2023 report lists both explanations among its Merit answers.

How did it go?

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