AS 91526 · 2025 paper · DC circuits

Question 1(c)(ii) Merit to Excellence

Mereana has a caravan with a simple battery-powered lighting circuit of total resistance 6.00 Ω. The battery has an EMF of 12.6 V and an internal resistance of 0.100 Ω.

R	6.00 Ω
ε	12.6 V
r	0.100 Ω

Explain, using physics principles, why the graph has the shape you drew.

The 2025 paper, page 3 ↗ Marking schedule, page 2 ↗

Work it out

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

1 As current flows, what happens to the charge on the plates?
Charge flows off the plates, so Q falls.
2 How does the capacitor’s voltage depend on its charge?
V = Q / C, and C does not change, so the capacitor’s voltage falls with Q.
3 What pushes the current through the 6.00 Ω resistor?
The capacitor’s voltage does: I = V / R. A smaller voltage means a smaller current.
4 Why does the curve flatten out instead of falling in a straight line?
Current is the rate at which charge leaves. A smaller current drains the charge more slowly, so V and I fall more slowly still. The rate of fall is always in proportion to what is left, and that is what makes it exponential.

Answer Q falls, so V = Q / C falls, so I = V / R falls. A smaller current drains the charge more slowly, so each drop is smaller than the one before: an exponential decay towards zero.

What the marker wanted

Achieved One idea: the current decreases, or the capacitor’s voltage falls as its charge falls.
Merit Together with the graph from (i), showing the right time constant, 0.7 A and 0.26 A: says that the capacitor’s voltage and the current both fall as Q falls.
Excellence The graph with the one-time-constant value plotted. Merit lists the facts; Excellence links them: the current falls BECAUSE the charge (and so the voltage) falls, and that is why each drop is slower than the last.

The schedule marks (c)(i) and (c)(ii) together as one item, so Merit and Excellence here depend on your graph from (i) as well.

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

Common mistake

Explaining a capacitor that is charging. This one is emptying, with nothing pushing charge back on. NZQA’s 2025 report lists mixing up charging and discharging among the common reasons for Not Achieved.

How did it go?

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