AC vs DC

AC vs DC at a glance

Property	DC	AC
Direction	Constant	Reverses periodically
V vs t	V = V_constant	V = V_peak·sin(ωt)
Sources	Batteries, solar, fuel cells	Generators, power grid
Voltage transformation	Hard (DC-DC converter)	Easy (transformer)
Long-distance transmission	HVDC (high voltage DC)	HVAC
Storage	Easy (batteries)	Indirect (rectify, then store)
Power	P = VI	P = V_RMS·I_RMS·cos(φ)
Inductors and capacitors	Open/short at steady state	Frequency-dependent impedance

RMS, peak, and average

For sinusoidal AC: V(t) = V_peak·sin(ωt).

Quantity	Definition	Relation
Peak (V_max or V_p)	Maximum value	—
Peak-to-peak (V_pp)	From peak positive to peak negative	V_pp = 2·V_peak
RMS	Root-mean-square; equivalent DC for power	V_RMS = V_peak/√2 ≈ 0.707·V_peak
Average (rectified)	Average of |V|	V_avg = (2/π)·V_peak ≈ 0.637
Average (raw)	Time-averaged	0 for symmetric AC

Common AC values

System	RMS	Peak	Frequency
US household	120 V	170 V	60 Hz
EU household	230 V	325 V	50 Hz
3-phase residential US	240 V	340 V	60 Hz
Industrial 3-phase	480 V (US)	—	60 Hz
Transmission	110 kV - 1.2 MV	—	50/60 Hz

JavaScript — AC/DC calculations

// RMS conversions
function peakToRMS(V_peak) { return V_peak / Math.sqrt(2); }
function rmsToPeak(V_RMS) { return V_RMS * Math.sqrt(2); }

// 120V outlet
console.log(`120V RMS = ${rmsToPeak(120).toFixed(0)} V peak = ${(2 * rmsToPeak(120)).toFixed(0)} V_pp`);

// AC power for resistive load
function acPowerResistor(V_RMS, R) {
  return V_RMS * V_RMS / R;
}

// 120 V outlet on 100 W bulb (R = 144 Ω)
console.log(`120V on 144Ω: ${acPowerResistor(120, 144).toFixed(0)} W`);

// AC current at given V_RMS through R
function acCurrent(V_RMS, R) {
  return V_RMS / R;
}

// Power factor in AC
function realPower(V_RMS, I_RMS, powerFactor) {
  return V_RMS * I_RMS * powerFactor;
}

// Apparent power vs real
function apparentPower(V_RMS, I_RMS) { return V_RMS * I_RMS; }

// Bridge rectifier output voltage (after diodes drop)
function bridgeRectifierDC(V_AC_peak, diode_drop = 1.4) {
  // Two diodes in path → 1.4 V drop per cycle
  return V_AC_peak - diode_drop;  // approximate
}

console.log(`120V AC peak (170V): rectified = ${bridgeRectifierDC(170).toFixed(0)} V DC`);

// HVDC vs HVAC efficiency comparison
function transmissionEfficiency(P_load, V_line, R_line, X_line = 0) {
  // For DC: only R matters
  // For AC: X (reactance) matters too, plus skin effect, etc.
  const I = P_load / V_line;
  const lossDC = I * I * R_line;
  return {
    dcLoss: lossDC,
    dcEff: 1 - lossDC / P_load
  };
}

// 1 GW over 1000 km at 800 kV
console.log(transmissionEfficiency(1e9, 800e3, 50));
// HVDC excellent for long distance

// Inductor in DC vs AC
function inductorImpedance(L, frequency_Hz) {
  return 2 * Math.PI * frequency_Hz * L;  // Ω
}

console.log(`100mH at 0 Hz (DC): ${inductorImpedance(0.1, 0)} Ω`);     // 0 (short circuit)
console.log(`100mH at 60 Hz: ${inductorImpedance(0.1, 60).toFixed(2)} Ω`);  // 37.7
console.log(`100mH at 1 MHz: ${inductorImpedance(0.1, 1e6).toFixed(0)} Ω`); // 628,318

// Capacitor in DC vs AC
function capacitorImpedance(C, frequency_Hz) {
  if (frequency_Hz === 0) return Infinity;
  return 1 / (2 * Math.PI * frequency_Hz * C);
}

console.log(`1µF at 0 Hz: ${capacitorImpedance(1e-6, 0)} Ω`);  // ∞ (open)
console.log(`1µF at 60 Hz: ${capacitorImpedance(1e-6, 60).toFixed(0)} Ω`);
console.log(`1µF at 1 MHz: ${capacitorImpedance(1e-6, 1e6).toFixed(2)} Ω`);

Where each shines

• AC dominates. Power transmission and distribution; large motors; appliances drawing AC directly.
• DC dominates. Electronics (inside computers, phones), batteries, solar, EVs.
• HVDC. Long-distance transmission (China, Europe interconnects), undersea cables, large solar farms.
• Mixed. Most modern systems convert between AC and DC. Phone charger: AC in → AC step-down → rectified to DC.
• Audio. Audio is AC (analog signals); digital audio is encoded data but speakers driven by analog AC.
• Industrial 3-phase. Three-phase AC for motors, large heating elements, factory power.
• EVs and renewables. Solar, batteries are DC; needs inverter to feed AC grid.

Common mistakes

• Confusing RMS and peak. 120 V is RMS; peak is 170 V. Most equipment ratings are RMS.
• Forgetting frequency dependence. Inductors and capacitors behave very differently at DC vs different AC frequencies.
• Treating AC as just "rotating DC". AC waveform matters — sinusoidal vs square, harmonic content, power factor — all affect circuit behavior.
• Mixing AC and DC analysis. Use phasors for AC analysis; vectors for DC. Different mathematical frameworks.
• Ignoring polarity for DC, phase for AC. DC has +/-. AC has phase relationships between V and I (for reactive loads).
• Using DC formulas for power factor < 1. Real power ≠ V_RMS·I_RMS for reactive AC loads. Power factor must be included.