[1], [2], [3] Alternating current (AC) is a variable electric current flow, drawn as a sine wave.
Starting at zero, it grows to its max, peak voltage, goes to zero then to its minimum, and so on.
AC is the most common electricity type for homes (lights, refrigerators, TVs) and businesses as it’s easy to carry in long distances. Power stations makes AC for efficiency to send over power lines and transformers easily increase/reduce them for many needs.
Vpk or Vpkpk is signal processing and computer base
Vrms = power transmission
Vrms is kinda average or aggregate
aggregate: collection, mass
Vrms is often 120 V
Each wave take some time (T; period or time)
all period have the same time
frequency is 1/T
Canada general frequency: 1 Hz
full period: capital 'T', half period: lowercase 't'.
The AC in a circuit varies with time formula is: V = V0 sin(2*πf*t)
V0 = peak voltage
f = frequency
t = instantaneous current at time t, in seconds
Name origin AC gets its name by alternating direction (flowing forth/backward)
The peak value (Vp/Vpk) is the voltage at peak of sine curve (half a sine curve).
Peak voltage formula: Vp = √2 * Vrms
E.g. 1# What is the period (T) of the AC current?
1.1# What is the RMS (root mean square) value of the current?
1.2 What's the current at 5 ms?
Vp sine waves change in polarity and direction.
Without clipping/filtering, it has the same max voltage on either side of the 0 line.
This graph's Vp = 40 V: 1 side is +40 V, the other is -40 V.
Its peak-to-peak voltage (Vpk-pk) is 80 V. Note the voltage level changes always between the 2 points.
40 V isn't constant.
The voltage measured by a meter is the root mean squared (RMS/Vrms) value.
Vpk = Vrms*√2 = 40*√2 = 56.57 V
Vpk-pk = 40*2√2 = 113.14 V
While a vpk is a half wave, a peak-to-peak (Vpk-pk) value is a full AC sine wave: Vpk*2, Vpk*2, or Vavg * π
Root mean squared (RMS) is the square root of the signal squared's average value and the average absolute voltage, no matter the polarity.
Sine waves occur so fast we see a constant value. It's a means to calculate the average value.
Vrms formula: [π/(2*√2)]*Vavg or Vrms = Vp/√2
VRMS is the value when viewing a meter reading.
The average voltage of a sine wave over a full period (or any integer periods number) is 0 V as the positive and negative halves of the cycle cancel each other out.
A sine wave is symmetric about the time axis, meaning the integral (area under the curve) over one full period is zero.
period T = 40
T = 40ms is irrelevant to the average voltage as it only affects frequency or RMS calculations.
The average voltage is zero as a sine wave is symmetrical. Its positive and negative halves cancel each other out over a full cycle. E.g. If voltage goes to +9V at a point then -9V. The net effect averages to zero.
If plotted as a sine wave on a graph, the area under the curve (integral) sums to zero since the positive and negative areas are equal.
Notes:
Myth: "AC has no voltage because the average is zero."
Truth: The instantaneous voltage is real (e.g., 9V peak), but the long-term average is zero.
Myth: "AC can't power devices because it keeps reversing."
Truth: Many devices (like light bulbs) respond to the magnitude of voltage, not its direction.
The formula for a sine wave's average voltage over a full cycle or the average voltage of a sinusoidal AC signal on a full cycle:
Vavg = average voltage
A = amplitude (peak voltage)
T = period (time of a full cycle)
ω = angular frequency (ω = 2π f ω=2πf)
f = frequency
sin(ωt) = sine wave function describing how voltage varies overtime
∫ = integral - sums up the voltage at all tiny instant (dt) over a full cycle (0 to T). Dividing by T gives the function's average value.
Solving
As ω = 2π/T, the integral becomes
The integral of sin(ωt) is
Substitute ω = 2π/T
A pure sine wave over a full period's average voltage: V(t) = A sin(ωt + ϕ)
ω = 2π/T - angular frequency
ϕ = phase shift
As a sine wave's positive and negative halves cancel each other out over a full cycle.
E.g. A sine wave's amplitude is 9V. A full period's time of the wave is 40ms.
What is the average voltage of the AC source between 0s and 40ms?
Since ω = 2π/T
ϕ is the phase shift (assumed as 0 V), so it's
A sine wave's average voltage over a full period is zero, as the positive and negative halves cancel each other out.
So Vavg = 0 V
Direct current (DC) is constant electricity flow, drawn as a straight line, unlike AC current.
To tell if a circuit is AC or DC:
A DC circuit has a battery (lines) as power source.
An AC circuit has a oscilloscope (a wave in a circle) as power source.
AC generators/alternators convert mechanical energy into AC energy, based on electromagnetic induction principle, where a conductor (often a coil) rotates in a magnetic field, inducing an alternating current in a conductor.
AC generators have 2 main types:
Synchronous generators/Aaternators make AC power at constant frequency. The rotor rotates at the same speed as the magnetic field, synchronizing with the grid frequency (e.g., 50Hz or 60Hz). Often for power plants and wide-scale electricity generation.
Induction generators are often used for smaller, less controlled applications, where the mechanical input is supplied by an external source like a wind turbine or a water wheel. Its rotors don't rotate at the same speed as magnetic field, causing induction in the stator coils.
How it works [5] In AC generators, copper wires (in red; left) connect to wire coils.
Basic generators have a magnet rotating by its + and - poles: the poles push/pull electrons in the copper coils and wires.
The magnet's magnetic field varies alot so as the magnet passes a coil, the coil gets its magnetic field's intensity (0 to its max intensity)
intensity: electrical amount flowing at a point in a circuit per time unit, measured in amps
Each magnet's full rotation makes a sine wave.
Split, single, 3-phase are types of electric power distributions using AC, with phases.
phase: timing of AC waves as they oscillate between positive and negative cycles.
Single phase electricity (1φ) has a connection to a generator's single phase, just 1 sine wave.
3-phase electricity has a connection to all 3 phases, 3 sine waves.
Split phase electricty has a center-tap transformer splits a single phase into 2, giving 2 hot wires in a neutral.
Phases are wire coils inserted into the generator at 120° apart, so the coils get peak rotating magnetic field at various times, giving the 3 phases.
Single phase have big gaps between peaks. 3-phase combines the waves to fill the gaps and create more power.
Most countries use single-phase electricity.
Big commercial building (mainly Europe) use 3-phase electricity.
North American homes use split phase electricity.
Since electricity must go back at its source, current either goes:
between phases as its polarities flow forth/backward at various times; or
to the neutral if excess flow (if a phase's load is unbalanced)
[3] E.g. Currents in power lines and household electricity coming from a wall outlet are alternating currents.
Most countries' standard current is 50 cycles per second (i.e. a frequency of 50 Hz.).; in the U.S. is 60 cycles a second (frequency of 60 Hz).
Frequency is how many times a wave (voltage/current) cycle repeats per second, measured in Hertz (Hz).
Common example: 50Hz or 60Hz, depending on the country.
Time (T) is the duration for a wave's full cycle, the inverse of frequency.
Time formula: T = 1/f
E.g. If f = 50Hz, time per cycle = 1/50 = 0.02 s = 20 milliseconds (ms)
Like in math, a sine wave cycle is 360°, but a full time rotation changes with frequency.
time = wave's period
wave's period (time) inverse frequency: f = 1/t
Time unit = second (s)
Frequency unit = Hertz (Hz)
E.g. 1 Hz = 1 cycle a second.
[5] Most of America uses 60Hz electricity--the sine wave repeats 60 times a second and polarity changes 120 times a second (+ to -).
[5] Most countries use 50Hz electricity--the sine wave repeats 50 times a second and polarity changes 100 times a second (+ to -).
E.g. The setting for the wave form here is 2.5 ms/div, meaning the X-axis per square has 2.5 ms.
T = 1/F
With formula: f = 1/t → t = 1/f
f = frequency
t = time
The whole sine wave occupies 8 squares on the x-axes:
8 x 2.5 ms = 20 ms
The frequency is: 1/20m = 50 Hz
1# E.g. This graph's wave period is 200 ms.
This gives a frequency of 5 Hz (1/200m)
What's the frequency of these waves?
2# An input frequency of 60 Hz.
t = 1/f = 1/60 = 16.67 ms
3# An input frequency of 1 kHz.
t = 1/f = 1/1000 = 1 ms
4# An input frequency of 5 kHz.
t = 1/f = 1/5000 = 200 us
5# If the period of the wave is 500 us.
t = 1/f = 1/500u = 2 kHz
6# If the period of the wave is 20 ms.
t = 1/f = 1/20m = 50 Hz
E.g. 1# A meter reads Vrms at 120 V.
Vpk = Vrms*√2
Vpk-pk = Vrms*2√2
So, Vpk = 120x√2 = 169.7 V and Vpk-pk = 169.7x2 = 339.4 V
E.g. 2# Volts/division per square (2 square's distance) = 2 V
Vpk = 4 x 2 = 8 V
Vpk-pk: 8 x 2 = 16 V
Vrms = 8 ÷ √2 = 5.66 V
[2] Direct current - Wikipedia
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[2.5]
[3] Alternating current & Direct current - Scientific Committees
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