Grade 12 Physical Sciences · Electricity and Magnetism

Calculate rms values and AC power

Calculate rms current or voltage with V_rms = V_max/√2, or the average power of an AC appliance (a 325 V peak gives about 230 V rms).

past paper questions use it: 10 past paper questions use it
videos: 4 videos

Learn it: calculate rms values and ac power

Pick one and watch it, then try the questions below. Videos load only when you tap play.

Grade 12 Electrodynamics AC Circuit Calculations: RMS voltage and RMS currentMiss Martins Maths and Science

Grade 12 Electrodynamics AC Calculations: EXAM PRACTICE RMS voltage and RMS currentMiss Martins Maths and Science

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 9.6 · November 2024 · Paper 1 · National (DBE) · 3 marks

The graph below shows how the induced current in a generator varies with time. Diagram for this question

9.6 Calculate the root-mean-square current delivered by the generator.(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: calculate rms values and ac power

Work each one out first, then open the memo and check every tick.

3. Question 9.2.2 · May/June 2025 · Paper 1 · National (DBE) · 4 marks
9.2 An AC generator produces a maximum output voltage of $340$ V. A $1200$ W electric kettle operates optimally when it is connected to this generator.

Answer the questions that follow.
9.2.2 Calculate the root mean square current passing through the kettle.(4)
Show the memo (4 ticks)Memo
1. ✓
  rms voltage $V_{r m s} = \frac{V _{ma x}}{2} = \frac{340}{2}$
  $= 240, 42$ V
  1 mark · Calculate rms values and AC power
2. ✓
  METHOD 1: Formula $P_{a v e} = V_{r m s} I_{r m s}$
  1 mark · Calculate rms values and AC power
3. ✓
  METHOD 1: Substitution $1200 = (240, 42) I_{r m s}$
  1 mark · Calculate rms values and AC power
4. ✓
  METHOD 1: Answer $I_{r m s} = 4, 99$ A
  1 mark · Calculate rms values and AC power
4. Question 9.2.2 · November 2023 · Paper 1 · National (DBE) · 3 marks
9.2 The circuit diagram below shows an electric kettle and a toaster connected to an AC source with an rms voltage of $220$ V. The ammeter, connecting wires and switches S $_{1}$ and S $_{2}$ have negligible resistance.

Answer the questions that follow.
When switch S $_{1}$ is CLOSED and switch S $_{2}$ is OPEN, the maximum current through the circuit is $3, 6$ A.
9.2.2 Calculate the root mean square current in the circuit.(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula $I_{r m s} = \frac{I _{ma x}}{2}$
  1 mark · Calculate rms values and AC power
2. ✓
  Substitution $= \frac{3 , 6}{2}$
  1 mark · Calculate rms values and AC power
3. ✓
  Answer with unit $= 2, 55$ A
  1 mark · Calculate rms values and AC power
5. Question 9.2.1 · May/June 2022 · Paper 1 · National (DBE) · 3 marks
9.2 A resistor Y is rated $220$ V, $100$ W and is connected to a $220$ V AC source, as shown in the circuit below.

Answer the questions that follow.
9.2.1 Calculate the resistance of resistor Y.(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula $P_{a v e} = \frac{V _{r m s}^{2}}{R}$
  1 mark · Calculate rms values and AC power
2. ✓
  Substitution $100 = \frac{22 0 ^{2}}{R}$
  1 mark · Calculate rms values and AC power
3. ✓
  Answer with unit $R = 484 Ω$
  1 mark · Calculate rms values and AC power
6. Question 9.3 · November 2025 · Paper 1 · National (DBE) · 5 marks
An AC generator operates a fan. The directions of the rotation of the coil and the induced current are shown in the simplified diagram below.
9.3 The resistance of the fan is $60 Ω$ and the maximum potential difference produced by the generator is $311, 11$ V. Calculate the cost of operating the fan for $1, 5$ hours if the cost of electricity is R3,33 per kWh.(5)
Show the memo (5 ticks)Memo
1. ✓
  Substitution into $V_{r m s}$ $V_{r m s} = \frac{V _{ma x}}{2} = \frac{311 , 11}{2} = 219, 99$ V
  1 mark · Calculate rms values and AC power
2. ✓
  Formula for average power $P_{a v e} = \frac{V _{r m s}^{2}}{R}$
  1 mark · Calculate rms values and AC power
3. ✓
  Substitution $P_{a v e} = \frac{219 , 9 9 ^{2}}{60} = 806, 59$ W $= 0, 80659$ kW
  1 mark · Calculate rms values and AC power
4. ✓
  Substitution into costcost $= P Δ t \times$ tariff $= 0, 80659 (1, 5) (3, 33)$
  1 mark · Calculate electrical power and energy
5. ✓
  Answer $=$ R4,03
  1 mark · Calculate electrical power and energy

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills