ESU of current to Coulomb per second
ESU
C/s
Conversion History
| Conversion | Reuse | Delete |
|---|---|---|
1 ESU (ESU of current) → 0.0000000003335641 C/s (Coulomb per second) Just now · Rounding: Up to 8 significant figures | Recalculate this conversion using your current rounding settings. |
Quick Reference Table (ESU of current to Coulomb per second)
| ESU of current (ESU) | Coulomb per second (C/s) |
|---|---|
| 1 | 0.0000000003335641 |
| 10 | 0.000000003335641 |
| 100 | 0.00000003335641 |
| 1,000,000 | 0.0003335641 |
| 1,000,000,000 | 0.3335641 |
| 3,000,000,000 | 1.0006923 |
Results rounded to a maximum of 8 significant figures
About ESU of current (ESU)
The electrostatic unit of current (ESU, also called the statampere) equals approximately 3.335640952×10⁻¹⁰ amperes under the traditional CGS-to-SI mapping used by this converter. It is the current unit of the CGS electrostatic system (CGS-ESU), in which Coulomb's law is written without a permittivity constant and electric charge is measured in statcoulombs (franklins). One statampere is the flow of one statcoulomb per second. The traditional mapping is 1 A = (c/10) statamperes, using the numerical speed of light c = 29,979,245,800 in cm/s, so 1 A maps to 2,997,924,580 statamperes. This is a conventional mapping, not a claim of an exact physical conversion to the post-2019 SI. The CGS-ESU system was used in early electrostatics and vacuum tube physics but is obsolete in applied engineering.
1 ESU of current ≈ 3.336×10⁻¹⁰ A — an extraordinarily small current. One ordinary ampere equals approximately 3×10⁹ ESU.
About Coulomb per second (C/s)
The coulomb per second (C/s) is a derived SI expression for electric current that makes the physical definition explicit: one ampere is exactly one coulomb of charge passing a point per second. The relationship I = Q/t links current (A), charge (C), and time (s). While C/s and A are numerically identical and dimensionally equivalent, the C/s form appears in physics textbooks and dimensional analyses where the derivation from charge and time is instructive rather than treating the ampere as primitive. In calculations tracking charge accumulation — capacitor discharge, electroplating, or battery coulomb-counting — expressing current in C/s clarifies the unit chain.
A capacitor delivering 1 C of charge over 1 second discharges at exactly 1 C/s = 1 A. A 500 mA USB charger transfers 0.5 C of charge each second.
ESU of current – Frequently Asked Questions
Why is the ESU of current so absurdly small compared to an ampere?
The ESU system was designed to make Coulomb's electrostatic law simple (no constants), which means its charge unit (the statcoulomb) is tiny relative to the coulomb. Since current is charge per time, the statampere inherits that smallness. Under the traditional mapping used here, one ampere maps to 2,997,924,580 statamperes — the numerical speed of light in cm/s divided by 10. In the reverse direction, multiply the statampere value by 10/c, or divide by 2,997,924,580, to obtain amperes.
What is a statampere and is it the same as an ESU of current?
Yes. Statampere, ESU of current, CGS electrostatic current, franklin per second and Gaussian current share the same current scale. This converter uses the same traditional mapping for all five names: 1 A maps to 2,997,924,580 statamperes. "Statampere" is the named form; "ESU of current" is the descriptive form. The "stat-" prefix comes from "electrostatic," just as the "ab-" prefix in the EMU system comes from "absolute."
Did the 2019 SI redefinition change the statampere?
No. The statampere remains one statcoulomb per second in the CGS system. What changed was the SI ampere: in 2019 it was redefined by fixing the elementary charge, replacing its earlier force-based definition. Vacuum permeability and permittivity are consequently no longer exact SI constants, so physical conversions between CGS electrical units and modern SI involve measured values and uncertainty. This converter retains the pre-2019 mapping of 1 A to 2,997,924,580 statamperes for consistent reference conversions; it does not apply modern measured corrections.
What role did the ESU system play in the discovery that light is electromagnetic?
When Weber and Kohlrausch measured the ratio of ESU to EMU charge in 1856, they got a number suspiciously close to the speed of light — about 3×10¹⁰ cm/s. Maxwell realized this was no coincidence: it meant electromagnetic disturbances propagate at light speed, proving light itself is an electromagnetic wave. A unit conversion exercise led to one of the greatest discoveries in physics.
What practical problem did the ESU system solve for 19th-century telegraph engineers?
Telegraph cables behaved like long capacitors — charge stored along the line distorted signals over transatlantic distances. The ESU system, built around Coulomb's law, made capacitance calculations straightforward: no permittivity constants, just geometry and charge. William Thomson (Lord Kelvin) used ESU-based analysis to diagnose and fix signal distortion on the first transatlantic telegraph cables in the 1860s.
Why were electrostatic and electromagnetic measurements historically done in separate labs?
Electrostatic experiments (rubbing rods, Leyden jars, spark gaps) involved high voltages and tiny charges, while electromagnetic work (coils, galvanometers, telegraph lines) involved low voltages and large currents. The equipment, techniques, and even the physicists were different. Each community built units natural to their measurements — ESU for electrostatics, EMU for electromagnetics — and it took decades after Maxwell to unify them into one coherent SI framework.
Coulomb per second – Frequently Asked Questions
Why bother writing coulombs per second when it is just amperes?
In dimensional analysis and physics derivations, C/s makes the relationship between charge and current explicit. When you are computing how much silver an electroplating bath deposits (Faraday's law), writing current as C/s reminds you that charge = current × time, which directly gives the mass deposited.
How many electrons is one coulomb?
One coulomb is approximately 6.242 × 10¹⁸ electrons — about 6.2 quintillion. At 1 C/s (1 A), that many electrons pass a point in your wire every single second. A USB cable charging your phone at 2 A carries 12.5 quintillion electrons per second. The numbers are staggering but the charges are tiny.
Is coulombs per second used in any real-world instrument or specification?
Not directly — every instrument reads in amperes or milliamperes. But coulomb-counting battery fuel gauges internally track charge in coulombs by integrating current over time: ∫I dt. The C/s framing appears in battery management system firmware and electrochemistry literature where charge balance matters.
How does Faraday's law of electrolysis use coulombs to predict metal deposition?
Faraday discovered that the mass of metal deposited at an electrode is directly proportional to the total charge passed (in coulombs). For silver, 107.87 grams deposit per 96,485 C (one Faraday). So a 10 A electroplating bath running for 1 hour passes 36,000 C and deposits about 40 g of silver. Thinking in C/s makes the calculation: current × time × atomic weight / (valence × 96,485).
How does coulomb counting work in battery management systems?
A shunt resistor or Hall sensor continuously measures current flowing in and out of the battery. The BMS integrates this current over time (summing C/s × Δt) to track net charge. Drift and measurement errors accumulate, so smart BMS designs periodically recalibrate against voltage-based state-of-charge estimates.