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AS 91526 · 2023 paper · capacitors

Question 1(b) Merit to Excellence

Practises Charging & discharging (RC)

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.

C185 nF
V1.50 V

In the charging circuit the battery has an internal resistance of 0.270 Ω; assume the rest of the circuit has none.

Sketch how the charge on the plates varies with time once the switch closes, plotting at least four points and showing the time constant and the maximum charge.

The 2023 paper, page 2 ↗ Marking schedule, page 1 ↗

Work it out

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

  1. 1 What resistance does the capacitor charge through?

    Only the battery’s internal resistance, 0.270 Ω, because the rest of the circuit has none.

  2. 2 Work out the time constant.

    τ = RC = 0.270 × 1.85 × 10−7 = 5.00 × 10−8 s. The grid’s time axis is in units of 10−8 s, so that is at 5.

  3. 3 What is the most charge it can hold, in the grid’s units?

    Qmax = CV = 2.78 × 10−7 C = 27.8 × 10−8 C. Draw it as a dashed line for the curve to approach.

  4. 4 How much of Qmax is on the plates after each time constant?

    Q = Qmax(1 − e−t/τ). With both axes in units of 10−8: t = 0, Q = 0; t = 5, Q = 17.5 (63%); t = 10, 24.0; t = 15, 26.4; t = 20, 27.2; t = 25, 27.6.

  5. 5 Now draw it.

    Plot the points and join them with a smooth curve: steep at first, then flattening, closing in on 27.8 without ever crossing it. Mark τ on the time axis and Qmax on the charge axis.
Answer A curve rising from zero and levelling off at Qmax = 27.8 × 10−8 C, passing through 17.5 × 10−8 C at τ = 5.00 × 10−8 s, then 24.0 at 10, 26.4 at 15 and 27.2 at 20 (both axes in units of 10−8).

What the marker wanted

  • Achieved One of: τ = 5.00 × 10−8 s, a curve of the right shape, or the charge at τ, 1.75 × 10−7 C.
  • Merit A curve that starts at zero and levels off at Qmax, with τ = 5.00 × 10−8 s and the charge at τ (17.5 × 10−8 C) both on it. One error is allowed.
  • Excellence The whole graph, with at least four points plotted correctly.

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

✕

Common mistake

Plotting the capacitance or the voltage where the charge should be: 63% of 1.50 V at t = τ, say. The schedule tells markers to look out for exactly this.

How did it go?

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