Electric Current

Definition

Electric current is the rate of charge flow:

I = dQ / dt

Units: amperes (A), where 1 A = 1 C/s.

For DC, I is constant in time. For AC, I varies periodically — typically I(t) = I_max·cos(ωt).

Conventional vs electron current

Conventional current — direction of POSITIVE charge flow. Goes from + to − terminal externally.

Actual electron flow — direction electrons move. From − to + terminal (opposite of conventional).

Both are equivalent; conventional is used in most engineering. Mathematically, ∂Q/∂t for positive charge flow direction.

Drift velocity

For a wire of cross-section A, with n free electrons per volume, drift velocity v_d:

I = n · e · A · v_d

For copper wire (n ≈ 8.5 × 10²⁸ /m³) carrying 1 A through 1 mm² cross-section:

v_d = I / (n·e·A) = 1 / (8.5e28 × 1.6e-19 × 1e-6) ≈ 7.4 × 10⁻⁵ m/s

About 0.07 mm/s — very slow! Electrons drift slowly but signal (electric field) travels near light speed.

Current density

Current per unit area:

J = I / A  (units: A/m²)

For copper, safe J ≈ 4-10 A/mm². Beyond this, wire heats too much.

AC vs DC

Property	DC	AC
Direction	Constant	Reverses periodically
Sources	Batteries, solar, fuel cells	Power grid, generators
Frequency	0 Hz	50 or 60 Hz (line); higher for special
Voltage transformation	Hard (needs DC-DC converter)	Easy (transformer)
Long-distance transmission	HVDC (high voltage)	HVAC (high voltage)
Storage	Easy (batteries)	Indirect (convert to DC for batteries)
Power = VI for resistor	P = VI	P_avg = ½·V_max·I_max for sinusoidal

Body currents and safety

Current	Effect on human
1 mA	Mild tingle
5 mA	Painful shock
10-20 mA	Cannot let go (tetanic muscle contraction)
50 mA	Severe pain, fibrillation possible
100 mA across heart	Fatal in <1 second
1 A	Severe burns, cardiac arrest, loss of consciousness
10 A	Cardiac arrest, severe burns, often fatal

Higher voltage isn't always more dangerous — current is what kills. But high V can drive more I through low body R (especially wet skin).

JavaScript — current calculations

// Drift velocity from current
function driftVelocity(I, A, n_free_electrons_per_m3, e = 1.602e-19) {
  return I / (n_free_electrons_per_m3 * e * A);
}

// Copper wire (n ≈ 8.5e28/m³), 1 A through 1 mm² cross-section
console.log(`v_drift: ${(driftVelocity(1, 1e-6, 8.5e28) * 1000).toExponential(2)} mm/s`);
// 7.4e-2 mm/s

// AC RMS values
function rmsCurrent(I_max) { return I_max / Math.sqrt(2); }
function rmsVoltage(V_max) { return V_max / Math.sqrt(2); }
function powerAC_rms(V_rms, I_rms) { return V_rms * I_rms; }

// 120 V_RMS = 170 V peak
console.log(`120V RMS = ${(120 * Math.sqrt(2)).toFixed(0)} V peak`);

// AC vs DC heating equivalence
// AC at I_RMS heats same as DC at I_DC = I_RMS

// Power transmission loss
function transmissionLoss(P_load, V_line, R_wire) {
  const I = P_load / V_line;
  return I * I * R_wire;
}

// 100 MW at 120 V (silly) vs 230 kV
console.log(`100 MW at 120V over 100km of 1Ω wire: ${(transmissionLoss(100e6, 120, 1) / 1e6).toFixed(0)} MW lost`);
// 694 GW lost (impossible!)
console.log(`At 230 kV: ${(transmissionLoss(100e6, 230e3, 1)).toFixed(0)} W`);
// ~189 W — totally fine

// Battery discharge: how long can a 1500 mAh phone battery last?
function batteryLife(capacity_mAh, draw_mA) {
  return capacity_mAh / draw_mA;  // hours
}

console.log(`1500 mAh, 100 mA draw: ${batteryLife(1500, 100)} hours`); // 15 hours

// Current density limits for wire gauge
function maxCurrent(area_mm2, max_J = 4) {
  // J in A/mm² (typical safe)
  return area_mm2 * max_J;
}

console.log(`14 AWG (~2 mm²): ${maxCurrent(2)} A`);  // ~8 A safe (15A code limit)
console.log(`12 AWG (~3.3 mm²): ${maxCurrent(3.3)} A`); // ~13 A safe

// Charge from current and time
function chargeFromCurrent(I, t) {
  return I * t;  // C
}

// Number of electrons in 1 A·s = 1 C
console.log(`1 C = ${(1 / 1.602e-19).toExponential(2)} electrons`);
// 6.24e18

Where current matters

• Power transmission. Generation, grid, distribution, household.
• Electronics. Every device — current flows determine operation.
• Biology. Nerve signals, muscle contractions, electrical activity in tissues.
• Industry. Electroplating, electrolysis, welding, motors.
• Safety. Circuit breakers, GFCIs, fuses limit current to prevent fires/shock.
• Communications. Signals carried by varying current in conductors or modulated EM waves.
• Sensors. Many measurements (light, temp, pressure) → current changes for readout.

Common mistakes

• Confusing voltage with current. Voltage is potential difference (drives flow). Current is the actual flow rate. High V doesn't always mean high I (depends on R).
• Treating drift velocity as signal speed. Drift is slow (cm/hour). Signals travel near light speed via field propagation.
• Using peak vs RMS interchangeably. AC: V_peak vs V_RMS differ by √2. 120 V outlets are RMS; peak is 170 V.
• Forgetting that voltage is what kills... but current does the harm. Both matter; high V can drive lethal I through low R.
• Wrong current direction. Conventional current opposite to electron flow. Be consistent within an analysis.
• Treating wire as zero resistance. For sufficiently long or thin wires, resistance matters; voltage drops along length.