AC Theory
Sinusoidal waveforms, period, frequency, phase and amplitude; instantaneous, average, root mean square, peak and peak-to-peak values; triangular and square waveforms.
AC theory, summary notes
- 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.
- 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
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).
AC generation, the rotating coil
AC quantities concept map
AC Theory
AC theory quiz
AC Theory, quiz
1. The waveform shown has a peak value of 100 V. Its RMS value is approximately:
70.7 V141.4 V63.7 V2. In the two waveforms shown, B reaches its peak a quarter of a cycle after A. Waveform B is said to:
Lag A by 90°Lead A by 90°Be in phase with A3. An AC supply has a peak value of 340 V. Its RMS value is approximately:
240 V480 V216 V4. An AC waveform completes one cycle in 20 ms. Its frequency is:
50 Hz20 Hz0.02 Hz5. A sine wave has a peak value of 100 V. Its RMS value is approximately:
70.7 V63.7 V141 V6. The average value of a sine wave over a half cycle is:
0.637 × peak0.707 × peak1.11 × peak7. Aircraft AC systems typically operate at:
115 V, 400 Hz230 V, 50 Hz28 V, 60 Hz8. A waveform measures 340 V peak-to-peak. Its RMS value is approximately:
120 V240 V340 V9. If the period of a waveform is 2.5 ms, its frequency is:
400 Hz250 Hz40 Hz10. The RMS value of an alternating current is the value that:
Produces the same heating effect as an equivalent DCIs the maximum reached in a cycleIs the average over a full cycle