Describe period, frequency and peak value
Read the period, frequency and peak value of an alternating current or voltage from its cycle and waveform.
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 21. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use period, frequency, sine graphs, current, voltage, power, diodes, capacitors and SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the period of an alternating voltage?
What you will learn
- Define period and frequency for an alternating quantity
- Identify peak value from a waveform
- Convert between period and frequency
An alternating quantity repeats its cycle
An alternating current or voltage changes with time and reverses direction or polarity. One complete cycle returns the waveform to the same value and direction of change. The period T is the time for one cycle, measured in seconds.
Frequency f is the number of complete cycles per second, measured in hertz (Hz). Period and frequency are reciprocals: f = 1/T and T = 1/f. Read a time axis carefully: measure between equivalent points on successive cycles, such as peak to next peak.
Peak value is the maximum magnitude
The peak value x₀ is the greatest magnitude reached by the alternating current or voltage from its zero reference. A symmetric sinusoid with peak value 6 A ranges from +6 A to −6 A; its peak-to-peak value is 12 A, not 6 A.
On a graph, use the vertical scale to read the distance from zero to a crest or trough, and use the horizontal scale to read T. A larger peak-to-peak span does not change the definition of peak value: it is half that span for a symmetric waveform.
Pause and explain
A current has period 0.025 s. What is its frequency?
Worked example
A sinusoidal voltage completes 50 cycles in 1.0 s and reaches +325 V and −325 V. Find its frequency, period and peak value.
Show the worked solution
- Frequency is cycles per second.
- Use T = 1/f.
- Read the peak from zero, not peak-to-peak.
Answer f = 50 Hz, T = 1/50 = 0.020 s, and peak value V₀ = 325 V.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A sinusoidal current completes 25 cycles in 0.50 s. Calculate its frequency and period.
Give me a hint
Find cycles per second, then take the reciprocal for period.
Compare my reasoning
- f = 25/0.50 = 50 Hz.
- T = 1/f.
- T = 1/50 = 0.020 s.
f = 50 Hz and T = 0.020 s.
Look for these in your work
- Frequency calculated
- Reciprocal relation used
- Units stated
A symmetric voltage waveform reaches +12 V and −12 V. State its peak and peak-to-peak values.
Give me a hint
Measure each quantity relative to the zero line and between opposite extremes.
Compare my reasoning
- The crest is 12 V above zero.
- The peak value is therefore 12 V.
- Peak-to-peak span is 12 − (−12) = 24 V.
Peak value = 12 V; peak-to-peak value = 24 V.
Look for these in your work
- Peak measured from zero
- Both extremes used
- Values distinguished
A device receives an alternating current whose frequency changes from 50 Hz to 100 Hz. Compare the periods and describe the cycle rate.
Give me a hint
Use T = 1/f for both frequencies.
Compare my reasoning
- At 50 Hz, T = 1/50 = 0.020 s.
- At 100 Hz, T = 1/100 = 0.010 s.
- The second current completes twice as many cycles each second and each cycle takes half as long.
The period halves from 0.020 s to 0.010 s while the cycle rate doubles.
Look for these in your work
- Both periods calculated
- Period ratio compared
- Frequency meaning applied
Common mistakes
- Calling the positive-to-negative span the peak value
- Measuring half a cycle as the period
- Using f = T instead of f = 1/T
- Giving frequency in seconds rather than hertz
What can you explain now?
What is the period of an alternating voltage?
Compare with the explanation
Time for one complete cycle
Period measures one full repetition in seconds.
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Make it stick
How do period, frequency and peak value describe different features of an AC waveform?
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