Alternating Current Fundamentals (AC Fundamentals)

While Direct Current (DC) remains constant over time, Alternating Current (AC) reverses its direction periodically. The most common and mathematically pure form of AC is the sinusoidal waveform, which is generated by the rotation of alternators in power plants.

Sinusoidal Waveforms

A sinusoidal voltage waveform can be mathematically described as a function of time ($t$) as follows:

A similar equation applies to alternating current as well: $i(t) = I_m \sin(\omega t + \theta)$

Frequency and Period

A signal repeats itself over a specified time interval called the Period ($T$). The Frequency ($f$) is the number of cycles the signal completes in one second.

The standard power grid frequency is typically 50 Hz (in most parts of the world) or 60 Hz (in North America).

Root Mean Square (RMS) Value

Because AC signals change constantly and their average value over a full cycle is zero, we cannot use the simple average to calculate useful power. Instead, we use the RMS value, which is the equivalent DC value that would deliver the same average power to a resistor.

For a pure sine wave, the relationship between peak amplitude ($V_m$) and RMS value ($V_{rms}$) is:

$V_{rms} = \frac{V_m}{\sqrt{2}} \approx 0.707 V_m$

Engineering Check

When appliances or power supplies specify "220 V" or "120 V", these are almost always RMS values, not peak values. A 220 V AC system actually has voltage peaks reaching over 311 Volts! Engineers must design insulation and components to withstand these peak voltages, not just the RMS voltage.