A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Sinusoidal Voltages and Currents, RMS Values, and Oscilloscope Use — mark scheme explained
The short answer
In this section, we will explore sinusoidal voltages and currents, the concepts of root mean square (RMS), peak, and peak-to-peak values for sinusoidal waveforms. We will also discuss how to use an oscilloscope to measure these quantities and understand its basic controls.
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
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculation questions, show all steps clearly and use the correct formulas. For measurement questions using an oscilloscope, describe the process accurately and include units in your final answer. Always check your work for any arithmetic errors.
What the command words demand
- Calculate
- Perform a mathematical operation to find a specific value.
- Determine
- Find or establish the value of something using given data or formulas.
- Measure
- Use an instrument, such as an oscilloscope, to find the value of a quantity.
- Explain
- Provide a clear and detailed account of how something works or why it happens.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5 minutes for each question involving calculations or measurements with an oscilloscope. Ensure you have enough time to double-check your answers.
- Identify the peak value: V 0 = 10 V.0 marks
- Calculate the RMS value using the formula V rms = V 0 / √2:1 mark
- V rms = 10 V / √2 ≈ 7.07 V1 mark
- Calculate the peak-to-peak value using the formula V pp = 2V 0 :1 mark
- V pp = 2 × 10 V = 20 V1 mark
Final answer: RMS value: 7.07 V, Peak-to-peak value: 20 V
Work through every step correctly and you earn all 4 marks.
Another worked example
The RMS voltage of a sinusoidal waveform is 150 V. Calculate its peak and peak-to-peak values.
- Identify the RMS value: V rms = 150 V.0 marks
- Calculate the peak value using the formula V 0 = V rms × √2:1 mark
- V 0 = 150 V × √2 ≈ 212.13 V1 mark
- Calculate the peak-to-peak value using the formula V pp = 2V 0 :1 mark
- V pp = 2 × 212.13 V ≈ 424.26 V1 mark
Final answer: Peak value: 212.13 V, Peak-to-peak value: 424.26 V
Work through every step correctly and you earn all 4 marks.
Common mistakes
Confusing peak and RMS values.
Why it happens: Students often mix up the formulas for peak and RMS values, leading to incorrect calculations.
Fix: 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.
Why it happens: Students sometimes forget that the peak-to-peak value is twice the peak value, leading to incorrect results.
Fix: 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.
Why it happens: Students may not understand how the time base affects the display, leading to incorrect measurements of frequency or time intervals.
Fix: 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.
Why it happens: Students may not correctly interpret the voltage scale, leading to incorrect measurements of peak or RMS values.
Fix: 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.
Why it happens: Students may use incorrect formulas or mix up the relationships between these values, leading to errors in calculations.
Fix: 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.
Why it happens: Students may not use the trigger level control effectively, leading to unstable or unclear waveforms.
Fix: 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
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate AC Values | Find the RMS and peak-to-peak voltages from a given peak voltage of a sinusoidal signal. | 4 |
| Calculate Peak Voltage | Find peak and peak-to-peak voltages from a sinusoidal RMS value using standard formulas. | 4 |
| AC Current Values | Calculate the RMS and peak-to-peak values of a sinusoidal current from its peak value. | 4 |
| AC Voltage Values | Calculate the RMS and peak-to-peak voltages from a given peak voltage value. | 4 |
| Total across these question types | 16 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.