Sinusoidal waveforms — period, frequency, phase and amplitude; instantaneous, average, root mean square, peak and peak-to-peak values; triangular and square waveforms.
Notes
AC theory — summary notes
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Main ideas
An alternating quantity reverses direction periodically. One complete cycle is 360 electrical degrees.
Peak value V_p is the maximum. Peak-to-peak is 2 × V_p.
RMS (root mean square) is the effective value: V_rms = 0.707 × V_p, or V_p / √2. RMS is what meters read and what does the same heating work as an equivalent DC.
Average value over a half cycle is 0.637 × V_p.
Frequency f = 1 / T, in hertz. Angular velocity ω = 2πf.
Aircraft AC systems run at 115 V, 400 Hz — the high frequency allows smaller, lighter transformers and machines.
⚠ Exam trap: RMS = peak ÷ √2 (0.707), average = 0.637 × peak, and questions often quote peak-to-peak, which is twice the peak. Aircraft frequency is 400 Hz, not 50 or 60.
Key formulas
RMS value
V_rms = 0.707 × V_p = V_p / √2
Average value
V_av = 0.637 × V_p (half cycle)
Peak-to-peak
V_pp = 2 × V_p
Frequency and period
f = 1 / T (hertz)
Form factor
form factor = RMS / average = 1.11
Solved examples
A sine wave has a peak value of 100 V. Find its RMS and average values.
RMS = 0.707 × 100 = 70.7 V. Average = 0.637 × 100 = 63.7 V.
An oscilloscope shows a waveform of 340 V peak-to-peak. What is the RMS value?
Peak = 340 / 2 = 170 V. RMS = 0.707 × 170 = 120 V (approximately mains voltage).