AC/DC

Direct current flows one way; alternating current reverses direction many times a second. Learn sine-wave parameters, RMS, phase and phasors, three-phase basics, and why the world runs on AC but increasingly uses DC.

DC (direct current) keeps a constant polarity — batteries, solar panels and electronics use it. AC (alternating current) swings positive and negative in a sine wave, 50 or 60 times per second on the mains.

AC won the 'war of the currents' because transformers can step AC voltage up for efficient transmission and down for safe use. Today power electronics blurs the line: HVDC links, solar inverters, EV chargers and every phone charger convert between the two.

An analogy

DC is a river flowing steadily downhill. AC is the tide — water surging in and out. Both can turn a waterwheel; you just need the right wheel.

Describing a sine wave

A sine wave has a peak V_m, a frequency f (cycles per second) and a phase φ (where it starts). The mains in Europe/India is 230 V RMS at 50 Hz; in North America it is 120 V at 60 Hz.

Why RMS?

The RMS value is the DC value that would heat a resistor equally. 230 V RMS AC delivers the same power to a heater as 230 V DC, even though its peak is 325 V. Meters labelled 'true RMS' compute it correctly for any waveform; cheap meters assume a pure sine.

Phase and phasors

When two sine waves of the same frequency are shifted in time, the shift is expressed as a phase angle. A phasor represents each sine as a rotating arrow (magnitude = RMS value, angle = phase), turning differential equations into complex-number algebra — the foundation of AC circuit analysis.

Three-phase power

Three sine waves 120° apart deliver constant total power (no 100 Hz pulsation), need less conductor material for the same power, and create rotating magnetic fields for motors. In a star (Y) system V_line = √3 · V_phase: 400 V between lines and 230 V line-to-neutral.

Why DC is coming back

HVDC has no reactive power or skin-effect losses and no stability limit on long lines, so it wins beyond ~600 km overhead or ~50 km of submarine cable. Data centres, solar farms, batteries and EVs are native DC, and 380 V DC distribution avoids repeated AC/DC conversion.

Crest factor and non-sinusoidal waves

Crest factor = peak/RMS (1.414 for a sine). Square waves have 1.0; rectifier input currents can exceed 3. Meters, fuses and UPS ratings must account for crest factor, and harmonics are analysed with the Fourier series.

Formulas

• Sine wave: v(t) = V_m · sin(ωt + φ)
• Period & angular frequency: T = 1/f, ω = 2πf
• RMS of a sine: V_rms = V_m / √2 ≈ 0.707 V_m
• Average of rectified sine: V_avg = 2V_m / π ≈ 0.637 V_m
• Three-phase (star): V_line = √3 · V_phase

Worked example: Mains sine-wave parameters

Given: V_rms = 230 V; f = 50 Hz

Find: Peak, peak-to-peak, period and angular frequency.

• V_m = √2 × 230 = 325.3 V
• V_pp = 2 × 325.3 = 650.5 V
• T = 1/50 = 20 ms
• ω = 2π × 50 = 314.2 rad/s

Answer: v(t) = 325.3 sin(314.2 t) V, T = 20 ms

Worked example: Line voltage from phase voltage

Given: V_phase = 230 V (star-connected)

Find: Line-to-line voltage.

• V_L = √3 × V_ph
• = 1.732 × 230 = 398 V ≈ 400 V

Answer: ≈ 400 V

Common mistakes

• Wrong: Choosing a capacitor rated 250 V for a rectified 230 V supply. — Right: The peak is 325 V (plus tolerance) — use a 400 V or 450 V rated part.
• Wrong: Reading a distorted waveform with an average-responding meter. — Right: Use a true-RMS meter for non-sinusoidal voltage or current.

Applications

• Transmission: AC is stepped up to 132–765 kV by transformers for long-distance transmission and down to 400/230 V for homes.
• Electronics: Every device with a chip converts AC to low-voltage DC with a rectifier and regulator (or a switch-mode supply).
• HVDC interconnectors: Undersea links between countries use HVDC because long AC cables draw huge capacitive charging currents.

Key takeaways

• AC is described by peak, RMS, frequency and phase; V_rms = V_m/√2 for a sine.
• RMS is the heating-equivalent value used for all ratings and power calculations.
• Phasors turn sinusoidal analysis into complex arithmetic.
• Three-phase gives constant power; V_line = √3 V_phase in star.

Going further

• Complex (phasor) notation: Writing V = V_rms∠φ = V_rms·e^{jφ} turns the calculus of sinusoidal steady state into algebra: d/dt becomes multiplication by jω. Impedance Z = R + jX and complex power S = V·I* follow directly.
• Grid frequency as a balance indicator: Frequency falls when load exceeds generation and rises when generation exceeds load. Governors, synthetic inertia from inverters and under-frequency load shedding keep 50/60 Hz within tight bands.
• Symmetrical components: Any unbalanced three-phase set can be split into positive-, negative- and zero-sequence components. This Fortescue transformation is the tool used for fault analysis and protection relaying.