Electric charge is the physical property that causes particles to experience electromagnetic force. Comes in positive and negative. Like charges repel, opposite charges attract. Fundamental to all chemistry and electronics.

• 1 coulomb = 6.24×10¹⁸ electrons
• Proton: +1e, Electron: -1e
• Charge is conserved (never created/destroyed)
• Quantized in multiples of e = 1.602×10⁻¹⁹ C

Current (I) is flow rate of charge. Q = I × t. 1 ampere = 1 coulomb per second. Battery capacity in Ah is charge, not current. 1 Ah = 3600 C.

• Current = charge per time (I = Q/t)
• 1 A = 1 C/s (definition)
• 1 Ah = 3600 C (1 amp for 1 hour)
• mAh is charge capacity, not power

Batteries store charge. Rated in Ah or mAh (charge) or Wh (energy). Wh = Ah × Voltage. Phone battery: 3000 mAh @ 3.7V ≈ 11 Wh. Voltage matters for energy, not charge.

• mAh = milliampere-hour (charge)
• Wh = watt-hour (energy = charge × voltage)
• Higher mAh = longer runtime (same voltage)
• 3000 mAh ≈ 10,800 coulombs

Before understanding charge quantitatively, scientists explored static electricity and the mysterious 'electric fluid.' The invention of batteries enabled precise measurement of continuous charge flow.

• 1600: William Gilbert distinguishes electricity from magnetism, coins term 'electric'
• 1733: Charles du Fay discovers two types of electricity (positive and negative)
• 1745: Leyden jar invented — first capacitor, stores measurable charge
• 1785: Coulomb publishes inverse-square law F = k(q₁q₂/r²) for electric force
• 1800: Volta invents battery — enables continuous, measurable charge flow
• 1833: Faraday discovers electrolysis laws — links charge to chemistry (Faraday constant)

The coulomb evolved from practical definitions based on electrochemical standards to the modern definition tied to the ampere and second.

• 1881: First practical coulomb defined via silver electroplating standard
• 1893: Chicago World's Fair standardizes coulomb for international use
• 1948: CGPM defines coulomb as 1 ampere-second (1 C = 1 A·s)
• 1960-2018: Ampere defined by force between parallel conductors, making coulomb indirect
• Problem: Ampere's force-based definition was difficult to realize with high precision
• 1990s-2010s: Quantum metrology (Josephson effect, quantum Hall effect) enables electron counting

On May 20, 2019, the elementary charge was fixed exactly, redefining the ampere and making the coulomb reproducible from fundamental constants.

• New definition: e = 1.602176634 × 10⁻¹⁹ C exactly (zero uncertainty by definition)
• Elementary charge is now a defined constant, not a measured value
• 1 coulomb = 6.241509074 × 10¹⁸ elementary charges (exact)
• Single-electron tunneling devices can count electrons one-by-one for precise charge standards
• Quantum metrology triangle: voltage (Josephson), resistance (quantum Hall), current (electron pump)
• Result: Any lab with quantum equipment can realize the coulomb independently

The 2019 redefinition represents 135+ years of progress from electrochemical standards to quantum precision, enabling next-generation electronics and energy storage.

• Battery technology: More accurate capacity measurements for electric vehicles, grid storage
• Quantum computing: Precise charge control in qubits and single-electron transistors
• Metrology: National labs can independently realize coulomb without reference artifacts
• Chemistry: Faraday constant now exact, improves electrochemistry calculations
• Consumer electronics: Better standards for battery capacity ratings and fast charging protocols

• mAh to C shortcut: Multiply by 3.6 → 1000 mAh = 3600 C exactly
• Ah to C: Multiply by 3600 → 1 Ah = 3600 C (1 amp for 1 hour)
• Quick mAh to Wh (3.7V): Divide by ~270 → 3000 mAh ≈ 11 Wh
• Wh to mAh (3.7V): Multiply by ~270 → 11 Wh ≈ 2970 mAh
• Elementary charge: e ≈ 1.6 × 10⁻¹⁹ C (round from 1.602)
• Faraday constant: F ≈ 96,500 C/mol (round from 96,485)

Understanding battery ratings prevents confusion between charge (mAh), voltage (V), and energy (Wh). These rules save time and money.

• mAh measures CHARGE, not power or energy — it's how many electrons you can move
• To get energy: Wh = mAh × V ÷ 1000 (voltage is critical!)
• Same mAh at different voltages = different energy (12V 1000mAh ≠ 3.7V 1000mAh)
• Power banks: Expect 70-80% usable capacity (voltage conversion losses)
• Runtime = Capacity ÷ Current: 3000 mAh ÷ 300 mA = 10 hours (ideal, add 20% margin)
• Li-ion typical: 3.7V nominal, 4.2V full, 3.0V empty (usable range ~80%)

• Charge from current: Q = I × t (coulombs = amperes × seconds)
• Runtime: t = Q / I (hours = amp-hours / amps)
• Energy from charge: E = Q × V (watt-hours = amp-hours × volts)
• Efficiency adjusted: Usable = Rated × 0.8 (account for losses)
• Electrolysis: Q = n × F (coulombs = moles of electrons × Faraday constant)
• Capacitor energy: E = ½CV² (joules = ½ farads × volts²)

• Confusing mAh with mWh — charge vs energy (need voltage to convert!)
• Ignoring voltage when comparing batteries — use Wh for energy comparison
• Expecting 100% power bank efficiency — 20-30% lost to heat and voltage conversion
• Mixing up C (coulombs) with C (discharge rate) — totally different meanings!
• Assuming mAh = runtime — need to know current draw (runtime = mAh ÷ mA)
• Deep discharging Li-ion below 20% — shortens lifespan, rated capacity ≠ usable capacity

Coulomb (C) is the SI base unit for charge. Defined from ampere and second: 1 C = 1 A·s. Prefixes from pico to kilo cover all practical ranges.

• 1 C = 1 A·s (exact definition)
• mC, µC, nC for small charges
• pC, fC, aC for quantum/precision work
• kC for large industrial systems

Ampere-hour (Ah) and milliampere-hour (mAh) are standard for batteries. Practical because they relate directly to current draw and runtime. 1 Ah = 3600 C.

• mAh — smartphones, tablets, earbuds
• Ah — laptops, power tools, car batteries
• kAh — electric vehicles, industrial UPS
• Wh — energy capacity (voltage-dependent)

Elementary charge (e) is fundamental unit in physics. Faraday constant in chemistry. CGS units (statcoulomb, abcoulomb) in old textbooks.

• e = 1.602×10⁻¹⁹ C (elementary charge)
• F = 96,485 C (Faraday constant)
• 1 statC ≈ 3.34×10⁻¹⁰ C (ESU)
• 1 abC = 10 C (EMU)

All charge is quantized in multiples of elementary charge e. You can't have 1.5 electrons. Quarks have fractional charge (⅓e, ⅔e) but never exist alone.

• Smallest free charge: 1e = 1.602×10⁻¹⁹ C
• Electron: -1e, Proton: +1e
• All objects have N×e charge (integer N)
• Millikan oil drop proved quantization (1909)

1 mole of electrons carries 96,485 C of charge. Called the Faraday constant (F). Fundamental to electrochemistry and battery chemistry.

• F = 96,485.33212 C/mol (CODATA 2018)
• 1 mole e⁻ = 6.022×10²³ electrons
• Used in electrolysis calculations
• Relates charge to chemical reactions

Force between charges: F = k(q₁q₂/r²). Like charges repel, opposite attract. Fundamental force of nature. Explains all chemistry and electronics.

• k = 8.99×10⁹ N·m²/C²
• F ∝ q₁q₂ (product of charges)
• F ∝ 1/r² (inverse square law)
• Explains atomic structure, bonding

Every battery-powered device has a capacity rating. Smartphones: 2500-5000 mAh. Laptops: 40-100 Wh. Power banks: 10,000-30,000 mAh.

• iPhone 15: ~3,349 mAh @ 3.85V ≈ 13 Wh
• MacBook Pro: ~100 Wh (airline limit)
• AirPods: ~500 mAh (combined)
• Power bank: 20,000 mAh @ 3.7V ≈ 74 Wh

EV batteries rated in kWh (energy), but capacity is kAh at pack voltage. Tesla Model 3: 75 kWh @ 350V = 214 Ah. Massive compared to phones!

• Tesla Model 3: 75 kWh (214 Ah @ 350V)
• Nissan Leaf: 40 kWh (114 Ah @ 350V)
• EV charging: 50-350 kW DC fast
• Home charging: ~7 kW (32A @ 220V)

Electroplating, electrolysis, capacitor banks, UPS systems all involve large charge transfers. Industrial UPS: 100+ kAh capacity. Supercapacitors: farads (C/V).

• Electroplating: 10-1000 Ah processes
• Industrial UPS: 100+ kAh backup
• Supercapacitor: 3000 F = 3000 C/V
• Lightning bolt: ~15 C typical

Multiply mAh by 3.6 to get coulombs. 1000 mAh = 3600 C.

• 1 mAh = 3.6 C (exact)
• 1 Ah = 3600 C
• Quick: mAh × 3.6 → C
• Example: 3000 mAh = 10,800 C

Divide mAh by ~270 for Wh at 3.7V Li-ion voltage.

• Wh = mAh × V ÷ 1000
• At 3.7V: Wh ≈ mAh ÷ 270
• 3000 mAh @ 3.7V = 11.1 Wh
• Voltage matters for energy!

Runtime (h) = Battery (mAh) ÷ Current (mA). 3000 mAh at 300 mA = 10 hours.

• Runtime = Capacity ÷ Current
• 3000 mAh ÷ 300 mA = 10 h
• Higher current = shorter runtime
• Efficiency losses: expect 80-90%

3500 mAh battery. App uses 350 mA. How long until dead?

Runtime = Capacity ÷ Current = 3500 ÷ 350 = 10 hours (ideal). Real: ~8-9h (efficiency losses).

20,000 mAh power bank. Charge 3,000 mAh phone. How many full charges?

Account for efficiency (~80%): 20,000 × 0.8 = 16,000 effective. 16,000 ÷ 3,000 = 5.3 charges.

Deposit 1 mole of copper (Cu²⁺ + 2e⁻ → Cu). How many coulombs?

2 moles e⁻ per mole Cu. 2 × F = 2 × 96,485 = 192,970 C ≈ 53.6 Ah.

Your body has ~10²⁸ protons and equal electrons. If you lost 0.01% of electrons, you'd feel 10⁹ newtons of repulsion—enough to crush buildings!

Lightning bolt: only ~15 C of charge, but 1 billion volts! Energy = Q×V, so 15 C × 10⁹ V = 15 GJ. That's 4.2 MWh—could power your home for months!

Classic science demo builds charge to millions of volts. Total charge? Only ~10 µC. Shocking but safe—low current. Voltage ≠ danger, current kills.

Car battery: 60 Ah = 216,000 C, releases over hours. Supercapacitor: 3000 F = 3000 C/V, releases in seconds. Energy density vs power density.

1909: Millikan measured elementary charge by watching charged oil drops fall. Found e = 1.592×10⁻¹⁹ C (modern: 1.602). Won 1923 Nobel Prize.

Electron charge quantization so precise, used to define resistance standard. Accuracy: 1 part in 10⁹. Fundamental constants define all units since 2019.

mAh measures charge (how many electrons). Wh measures energy (charge × voltage). Same mAh at different voltages = different energy. Use Wh to compare batteries across voltages. Wh = mAh × V ÷ 1000.

Rated capacity is nominal, not usable. Li-ion: discharge from 4.2V (full) to 3.0V (empty), but stopping at 20% preserves lifespan. Conversion losses, heat, and aging reduce effective capacity. Expect 80-90% of rated.

Not simply capacity ratio. 20,000 mAh power bank: ~70-80% efficient (voltage conversion, heat). Effective: 16,000 mAh. For 3,000 mAh phone: 16,000 ÷ 3,000 ≈ 5 charges. Real-world: 4-5.

Elementary charge (e = 1.602×10⁻¹⁹ C) is the charge of one proton or electron. All charge is quantized in multiples of e. Fundamental to quantum mechanics, defines fine structure constant. Since 2019, e is exact by definition.

Yes! Negative charge means excess electrons, positive means deficit. Total charge is algebraic (can cancel). Electrons: -e. Protons: +e. Objects: typically near-neutral (equal + and -). Like charges repel, opposite attract.

Li-ion: chemical reactions slowly degrade electrode materials. Each charge cycle causes tiny irreversible changes. Deep discharge (<20%), high temperature, fast charging accelerate aging. Modern batteries: 500-1000 cycles to 80% capacity.