AC fundamentals
What you’ll learn
- What alternating current is, and why a generator makes a sine wave.
- Frequency and period: 60 Hz in North America, 50 Hz in most other places.
- Peak, peak-to-peak, RMS and average — and which one your meter shows.
- Why a 120 V circuit really swings to about 170 V and back every cycle.
Alternating current changes direction many times a second, and its voltage follows a smooth curve called a sine wave: up to a positive peak, back through zero, down to a negative peak, and back to zero again. In Canada and the US that happens 60 times every second. The 120 V you read on a receptacle is not the highest the voltage gets — it is a kind of average called RMS, and learning what that means is the first job of the second year.
Where the sine wave comes from
A generator spins a magnet past coils of wire (or a coil inside a magnetic field). As a pole sweeps toward a coil the voltage builds, it is strongest as the pole passes squarely across it, and it falls away as the pole leaves. Then the opposite pole comes round and the voltage does the same thing the other way. Plot that against the angle of the rotor and you get a sine wave: one full turn of a two-pole machine is one cycle, 360°. That is why AC is described in degrees — 90° is the positive peak, 180° is back to zero, 270° is the negative peak.
Frequency and period
Frequency is how many cycles happen in one second, measured in hertz (Hz). The grid in Canada and the US runs at 60 Hz; most of Europe, Asia, Africa and Australia runs at 50 Hz. Period is the time one cycle takes, and it is just the flip of frequency.
- T = 1 ÷ fperiod, seconds
- f = 1 ÷ Tfrequency, hertz
- 60 Hz → 16.7 ms50 Hz → 20 ms
A two-pole generator has to spin at 3,600 rpm to make 60 Hz (60 turns a second × 60 seconds). Keep that number in mind — it comes back when you meet motor speeds later this year.
Four ways to describe one wave
Because the voltage never sits still, “how many volts?” needs a qualifier. There are four answers, and each has a job:
| Value | What it is | For 120 V RMS |
|---|---|---|
| Peak | The top of the wave, from zero | 169.7 V |
| Peak-to-peak | Top to bottom — twice the peak | 339.4 V |
| RMS | The heating value; what meters and nameplates give | 120 V |
| Average (half-cycle) | The mean of one half of the wave | 108.1 V |
- RMS = peak × 0.7070.707 = 1 ÷ √2
- peak = RMS × 1.4141.414 = √2
- average = peak × 0.637one half-cycle
RMS is the DC voltage that would heat the same resistor the same amount. A kettle on 120 V AC boils exactly as fast as it would on 120 V DC. That makes Ohm’s law and the power law work on AC just as they did in first year — as long as you use RMS values and the load is resistive.
The voltage at any instant
At any angle θ in the cycle the voltage is the peak times the sine of that angle: v = Vpeak × sin θ. At 0° and 180° it is zero; at 90° it is the full positive peak; at 270° the full negative peak. One neat check: at 45°, sin θ is 0.707, so a 120 V supply is momentarily at exactly 120 V.
Worked examples
1. From the meter reading to the peak
- Your meter reads 240 V across a range receptacle.
- Peak = 240 × 1.414 = 339.4 V.
- Peak-to-peak = 2 × 339.4 = 678.8 V.
2. What the insulation sees on 347/600 V
- Canadian commercial buildings often run 347/600 V; the US equivalent is 277/480 V.
- Line-to-line peak on 600 V: 600 × √2 = 848.5 V. On 480 V: 480 × √2 = 678.8 V.
- Line-to-neutral peak on 347 V: 347 × 1.414 = 490.7 V. Every cycle, twice a cycle (once each way).
3. Time to the first peak
- At 60 Hz one cycle takes 1 ÷ 60 = 0.01667 s = 16.67 ms.
- The first peak is a quarter of the way through: 16.67 ÷ 4 = 4.17 ms.
- On 50 Hz: 20 ms per cycle, so 5 ms to the first peak.
4. The voltage 30° into the cycle
- 120 V RMS → 169.7 V peak.
- sin 30° = 0.5.
- v = 169.7 × 0.5 = 84.9 V.
Try one: a 208 V circuit — peak, and period on 60 Hz
Peak = 208 × 1.414 = 294.1 V. Period = 1 ÷ 60 = 16.7 ms (frequency does not depend on voltage).
En la obra
Tips from the job
- Every voltage on a nameplate, a drawing or your meter display is RMS unless it says otherwise. Peak only comes up when you are thinking about insulation, surge ratings and meter categories.
- A true-RMS meter reads the heating value of any waveform. A cheaper average-responding meter is only right on a clean sine wave — on drives, LED drivers and electronics it can read well off.
- A scope or a power-quality meter will show you the actual shape. Flat-topped sine waves are common in buildings full of electronics; that is distortion, not a broken supply.
- Before you meter anything, confirm your meter and leads are rated for the category and voltage — see meter safety and CAT ratings.
Common mistakes
- Treating 120 V as the highest the voltage gets. It peaks at about 170 V, and 600 V peaks at about 849 V.
- Mixing up the 0.637 (average of a half-cycle) and 0.707 (RMS) factors.
- Doubling the peak to get RMS, or forgetting peak-to-peak is twice the peak.
- Assuming every meter reads distorted waveforms correctly. Only a true-RMS meter does.
Check yourself
8 questions. Tap an answer — it is marked straight away and the reason opens under it. Get 80% or better and the lesson is ticked off on the year page.
Not started yet.
-
A 60 Hz supply completes how many full cycles each second?
Answer and why
B. Hertz means cycles per second. 60 Hz is 60 complete cycles — and 120 reversals of direction, two per cycle.
-
How long does one cycle of 60 Hz take?
Answer and why
C. Period = 1 ÷ frequency = 1 ÷ 60 = 0.0167 s = 16.7 ms. On 50 Hz it is 20 ms.
-
Your meter reads 120 V AC on a receptacle. What is the peak voltage?
Answer and why
C. Meters read RMS. Peak = RMS × 1.414 = 120 × 1.414 ≈ 169.7 V.
-
What is the peak-to-peak voltage of that same 120 V supply?
Answer and why
A. Peak-to-peak is twice the peak: 2 × 169.7 ≈ 339.4 V, from the top of the positive half-cycle to the bottom of the negative one.
-
What does the RMS value of an AC voltage tell you?
Answer and why
B. 120 V RMS heats a heater element exactly as much as 120 V DC would. That is why RMS is the number on nameplates and the one your meter shows.
-
The average of a full sine-wave cycle is…
Answer and why
C. The positive half and the negative half are mirror images, so over a whole cycle they cancel to zero. The 0.637 figure is the average of ONE half-cycle.
-
A 600 V system (RMS). What peak voltage does the insulation actually see every cycle?
Answer and why
B. 600 × 1.414 ≈ 848.5 V. Insulation and meter ratings have to live with the peaks, not just the RMS figure.
-
On a 120 V RMS supply, what is the instantaneous voltage 30° into the cycle?
Answer and why
B. v = Vpeak × sin θ = 169.7 × sin 30° = 169.7 × 0.5 ≈ 84.9 V.
Preguntas frecuentes
Why do we use AC instead of DC?
Mainly because a transformer can step AC up and down easily. High voltage moves power long distances with little loss; low voltage is safer to use. A transformer only works on a changing current, so AC won. AC also suits generators and induction motors, which are simple and rugged.
Why does North America use 60 Hz and Europe 50 Hz?
History, not physics: early equipment makers settled on different frequencies and the grids grew around them. Equipment built for one can behave differently on the other — motors turn about 17% slower on 50 Hz, and some transformers run hotter — so check the nameplate before using anything imported.
Is RMS the same as average?
No. Averaged over a full cycle a sine wave is zero. RMS (root-mean-square) is a special average that squares the values first, so negative halves count too. For a sine wave, RMS is 0.707 × peak; the half-cycle average is 0.637 × peak.
Ver también
- Inductance — the next lesson: what a coil does to AC.
- Single & three phase formulas — printable.
- Using a multimeter — reading AC volts safely.
- Seguridad del medidor y categorías CAT
- Ohm’s law and power — still true for RMS values on resistive loads.
- All second year lessons
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