AQA A-Level Physics: Sinusoidal Voltages and Currents, RMS Values, and Oscilloscope Use — mark scheme explained

The question

A sinusoidal voltage has a peak value of 10 V. Calculate its RMS and peak-to-peak values. [Paraphrased for study — not reproduced from any exam paper.]

Mark scheme, decoded

What each mark is really for — in plain English — and the wording trap that loses it.

• S1

  Identify the peak value: V 0 = 10 V.

• S2

  Calculate the RMS value using the formula V rms = V 0 / √2:

• S3

  V rms = 10 V / √2 ≈ 7.07 V

• S4

  Calculate the peak-to-peak value using the formula V pp = 2V 0 :

• S5

  V pp = 2 × 10 V = 20 V

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   Identify the peak value: V 0 = 10 V.

2. S2

   Calculate the RMS value using the formula V rms = V 0 / √2:

3. S3

   V rms = 10 V / √2 ≈ 7.07 V

4. S4

   Calculate the peak-to-peak value using the formula V pp = 2V 0 :

5. S5

   V pp = 2 × 10 V = 20 V

6. Final answer: RMS value: 7.07 V, Peak-to-peak value: 20 V

Common mistakes

• Confusing peak and RMS values. — Remember that the RMS value is calculated as V rms = V 0 / √2, where V 0 is the peak value. Practice using both formulas in different contexts.
• Forgetting to multiply by 2 for peak-to-peak values. — Always double-check your calculations and remember that V pp = 2V 0 . Practice with multiple examples to reinforce this concept.
• Incorrectly setting the time base on an oscilloscope. — Ensure you set the time base correctly by counting the number of divisions for one complete cycle and using the formula T = n × (time per division), where n is the number of divisions.
• Misinterpreting the voltage scale on an oscilloscope. — Always check the voltage scale setting and count the number of divisions accurately. Practice with different scales to become more familiar.
• Using the wrong formula for converting between peak, RMS, and peak-to-peak values. — Memorize the correct formulas: V rms = V 0 / √2, V pp = 2V 0 . Practice using them in various scenarios to reinforce understanding.
• Failing to stabilize the waveform on an oscilloscope. — Adjust the trigger level to a point where the waveform is stable and clear. Practice with different signals to become more proficient.

Where the marks go

• Full worked solution (all marking points)4 marks

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