Electric Charge Converter

Convert between electric charge units including coulombs, ampere-hours, faradays, and elementary charges.

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Common Battery Capacities

Common Electric Charge Conversions

Battery Capacity Conversions

• 1000 mAh = 1 Ah = 3600 C
• 3000 mAh = 3 Ah = 10,800 C
• 10 Ah = 10,000 mAh = 36,000 C
• 100 Ah = 100,000 mAh = 360,000 C (car battery)

Electrochemistry Calculations

Using the Faraday constant F = 96,485.33 C/mol:

• Charge to deposit 1 mole of metal ions:
• Ag⁺ + e⁻ → Ag: 1 Faraday = 96,485 C
• Cu²⁺ + 2e⁻ → Cu: 2 Faradays = 192,971 C
• Al³⁺ + 3e⁻ → Al: 3 Faradays = 289,456 C

Static Electricity Examples

• Walking on carpet: ~1 µC (can cause spark)
• Touching doorknob (shock): ~10-100 nC
• Van de Graaff generator: ~100 µC
• Thundercloud: ~15-350 C
• Lightning bolt: ~1-50 C transferred

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About Electric Charge

Electric charge is a fundamental property of matter that causes it to experience electromagnetic forces. It's the physical property responsible for electrical phenomena and is conserved in all interactions.

The Coulomb (C)

The coulomb (C) is the SI unit of electric charge, named after French physicist Charles-Augustin de Coulomb. Since 2019, it is defined in terms of the elementary charge:

1 C = 6.241509074 × 10¹⁸ e

Historically, it was defined as: 1 C = 1 A × 1 s (the charge transported by 1 ampere in 1 second)

Elementary Charge (e)

The elementary charge (e) is the magnitude of electric charge carried by a single proton or the negative of an electron:

e = 1.602176634 × 10⁻¹⁹ C (exact, 2019 definition)

All electric charge in the universe exists in integer multiples of the elementary charge (charge quantization).

Faraday Constant (F)

The Faraday constant (F) is the charge of one mole of electrons (Avogadro's number of elementary charges):

F = 96,485.33212... C/mol

It's calculated as: F = N_A × e (Avogadro's number times elementary charge)

Named after Michael Faraday, it's fundamental in electrochemistry for calculating the amount of substance deposited or dissolved during electrolysis.

Battery Capacity - Ampere-hours (Ah)

Battery capacity is commonly measured in ampere-hours (Ah) or milliampere-hours (mAh):

• 1 Ah = charge delivered by 1 ampere for 1 hour = 3600 coulombs
• 1 mAh = 1/1000 Ah = 3.6 coulombs

Important: Ah measures charge (quantity), not energy. To get energy (Wh), multiply by voltage:

Energy (Wh) = Capacity (Ah) × Voltage (V)

Example: A 3000 mAh smartphone battery at 3.7V = 3 Ah × 3.7 V = 11.1 Wh energy

Faraday's Laws of Electrolysis

First Law: The mass of substance deposited/dissolved is proportional to the charge passed:

m = Q × M / (n × F)

• m = mass (grams)
• Q = charge (coulombs)
• M = molar mass (g/mol)
• n = number of electrons transferred
• F = Faraday constant (96,485 C/mol)

Second Law: For the same charge, masses deposited are proportional to equivalent weights.

CGS Units

• Abcoulomb (abC): CGS electromagnetic unit = 10 C
• Statcoulomb (statC): CGS electrostatic unit ≈ 3.336×10⁻¹⁰ C
• Franklin (Fr): Alternative name for statcoulomb

These units are rarely used today, replaced by SI units.

Charge Conservation

Electric charge is conserved in all physical processes:

• Charge cannot be created or destroyed
• Total charge in an isolated system remains constant
• When charges appear to be created, equal positive and negative charges appear together
• Example: Electron (−e) and positron (+e) created from photon, net charge = 0

Positive and Negative Charge

• Positive charge: Carried by protons, lack of electrons
• Negative charge: Carried by electrons
• Neutral: Equal positive and negative charges cancel
• Like charges repel, opposite charges attract

Practical Applications

• Battery ratings: Capacity in mAh determines runtime
• Electroplating: Faraday's laws determine coating thickness
• Electrolysis: Industrial production of metals and chemicals
• Capacitors: Store charge: Q = C × V
• Current measurement: I = Q / t (amperes = coulombs/second)
• Particle physics: Elementary charge as fundamental unit

Typical Charge Magnitudes

• Single electron: 1.602×10⁻¹⁹ C (elementary charge)
• Static spark: 10-100 nC
• Camera flash capacitor: ~1 mC
• AA battery capacity: ~9000 C (2500 mAh)
• Car battery: ~180,000 C (50 Ah)
• Lightning strike: 1-50 C
• Thundercloud: 15-350 C

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