Alternating Current
Everything so far pushed one way. The grid, audio and radio all wiggle — meet the sine wave and its honest average, RMS.
Builds on: 0.2 Voltage: Energy per Charge2.4 Inductors & Electromagnetism1.4 Power & Energy
Why the grid wiggles
Every circuit so far ran on DC — direct current, one steady direction. But the power in your wall is AC: the voltage swings smoothly positive, negative and back, 50 or 60 times a second. The reason is a lesson you’ve already had: transformers only work with changing current (Lesson 2.4). AC lets the grid step voltage up to hundreds of kilovolts for low-loss transmission (Ploss = I²R — high voltage means low current for the same power), then step it back down to safe levels at your street. DC won a few battles; AC won the war for distribution.
Anatomy of a sine wave
The natural shape of AC is the sine wave — it’s what a coil spinning in a magnetic field produces automatically. Three numbers pin one down:
- Peak (Vp): the highest instantaneous value. Peak-to-peak is the full swing, 2Vp.
- Frequency (f): cycles per second. Mains: 50 Hz (Europe) / 60 Hz (North America). Audio: 20 Hz–20 kHz. Radio: kHz to GHz.
- Phase: where in its cycle a wave is, relative to another — it mattered already in your filter’s future and matters hugely in AC power.
RMS: the honest average
What’s “the” voltage of a wave that spends its life changing? The plain average of a sine is zero — useless. The meaningful average asks: what DC voltage would heat a resistor equally? That’s the root-mean-square value, and for sines it comes out beautifully simple:
Every AC rating you meet — mains voltage, multimeter AC readings, amplifier power — is RMS unless stated otherwise. All your Unit 1 power formulas work unchanged with RMS values: P = Vrms·Irms for a resistive load.
A microphone turns pressure waves into small AC voltages; radio stations are AC at millions of hertz; the data lines in your computer are fast-switching waveforms. From this unit on, think of AC not just as power but as signals — the rest of the advanced course is about shaping and processing them.
⚡ Lab — The Waveform Machine
A live sine on the scope, with its peak and RMS lines marked.
- Sweep the frequency from 10 to 200 Hz and watch cycles crowd into the fixed window.
- Confirm the green RMS line always sits at 70.7% of the peak.
- Set Vp = 12 V: what would a DC voltmeter’s “equivalent heating” reading be?