# Is the coulomb unit a constant or does it depend on the wire

I'm completely new to electronics, and I'm a bit lost on the definition of a coulomb. I tried to find a decent definition, but they all seem to equate to something like:

The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is equal to the electric charge delivered by a 1 ampere current in 1 second and is defined in terms of the elementary charge e, at about 6.241509×1018 e.

So the definition here is effectively defining a coulomb as a constant by saying C = 6.241509×1018 × e and since e is a constant then a Coulomb is a constant derived from it.

The reason that I'm confused is because the definition also says:

It is equal to the electric charge delivered by a 1 ampere current in 1 second

But, doesn't the charge delivered by a current in a second depend on the resistance of the circuit that the current is running through? If I'm running 1 amp through two different gauges of wire, then doesn't the resistance of the wire alter how much charge can flow in a second?

• Commented Jul 31 at 8:01
• Your definition is for one coulomb, which is an amount of charge different from any other amounts of coulombs. There's nothing magic about this. It's the same as saying one pound, or one meter. Commented Jul 31 at 17:44

If the current is 1A then 1C/second flows. The higher the resistance of the wire the more power is lost in the wire (a thin wire may get very hot), but the rate of flow of charge is exactly the same.

It will take more voltage to cause 1A to flow through the wire if the wire has high resistance.

• Oh, this makes sense - so one Coulomb is effectively just the 6.241509×10^18 * e constant, and I was overcomplicating it by attempting to factor the resistance of the wire [or the configuration of the circuit as a whole]. So the "The higher the resistance of the wire the more power" part isn't directly related to Coulomb calculation, but it would relate to the efficiency/power factor of the circuit? Commented Jul 31 at 1:01
• 1C is the charge of 6.241509×$10^{18}$ electrons. No * e. Commented Jul 31 at 1:28
• Yes, power loss. "Power factor" is a term with specific meaning in AC circuits, so not applicable here, by convention. Note too that e is the charge of one electron so you can think of an imaginary boundary in the wire and the ~6x10^18 is the net count of electrons that meander through that boundary every second when 1A flows. Commented Jul 31 at 1:29

1 C is the charge of 6.241509×$$\10^{18}\$$ electrons.

This means the charge of one electron is 1.60217663×$$\10^{-19}\$$ coulombs.

# History

In the olden days¹, units of measure were defined by a physical object, the unit prototype. For the metric/SI systems², there were prototypes for metre, kilogram, etc.

For example, the kilogram prototype was a physical object made of a platinum-iridium alloy. It was used as the standard for defining the kilogram since its creation in 1889. The most significant change came during the 26th General Conference on Weights and Measures (CGPM) in November 2018, where it was decided to redefine the kilogram in terms of fundamental constants of nature rather than a physical object. It was effectively the last prototype of unit of measure used.

Since then, we use physical constants to define out units of measurement.

The Kilogram prototype

# The physical constants era

Now, we use physical constants to derive sizes of the units. Physical prototypes and standard reference materials are still used to calibrate instruments that do not need extreme precision. The balance used in your favourite grocery store is not calibrated using advanced physical experiments, but using a (typically certified) copy of a prototype of the unit.

For example:

• The meter is defined by the distance that light travels in a vacuum in 1/299,792,458 seconds.

• Kilogram is defined by a specific measurement on the Kibble balance.

The coulomb is not any different! We can say the coulomb unit is *the electric charge delivered by a current of 1 ampere in one second. But to be precise, the official definition is³:

• 1 coulomb is 1/(1.602176634×10–19) elementary charges,

given that the elementary charge is a charge of a single proton or the negative charge of a single electron.

# Footnotes

¹ Even before that, units were defined quite arbitrarily – by using dimensions of human body parts etc. Many cultures used also parts of statues as the prototypes. One notable example is the use of the "cubit," an ancient unit of length that was based on the forearm's length from the elbow to the tip of the middle finger. In some cases, the cubit was represented or standardized using a statue or a carved figure, where the dimensions of the statue's arm would serve as a reference for this measurement. Statues, particularly those of significant cultural or religious importance, were often constructed with precise proportions, making them suitable for establishing standard units.

² Nobody uses imperial units, right? It is possible that I am not right.

³ This answer does not provide literal definitions; they were reworded a little bit.

Your confusion may originate from somewhat reciprocal definition of charge and current.

Electrical current is a rate of change in time.

Any rate of chage is defined as:

$$R=\frac{dN}{dt}$$

where N is (local) quantity and t is time. (d means differential, you can think of it as infinitisemally small change)

In case of currents (water flow, electric current,...) the change happens usually through defined cross-section of [river, wire,...] from one side of the section to the other.

The problem is that unit of electric current (ampére) is base SI, while coulomb is not.

Working our case for I=1 and t going from t0=0 to t1=1 s:

$$I=\frac{dQ}{dt}\Rightarrow dQ=1\cdot dt\\Q=\int_{t_0}^{t_1}I\cdot dt=I\cdot(t_1-t_0)$$

So one C is ammout of charge flowing through a cross-section at 1 A for 1 s. Also it means one C is ammout of charge flowing same section at 2 A for 1/2 s.

Of course 1 C is a constant. It is a unit. Actually it is a constant (one) multiplied by unit of measure (coulomb)

The catch in your confusion are consequences of variables you can directly control/choose (voltage, power, resistance) and those you can not (charge, current). For constant voltage (battery) but different conductor (different resistance) you get different currents flowing through it. If you want to charge 1 C using that current you need to accomodate the time for that condition.

There are fake units, for example kgF. It is defined as force that keeps 1kg weight in equilibrium. The catch is that 1kgF in newtons at pole is not equal to same value in newtons on equator because of Earth's shape and rotation.

• Tip: SI units named a person have their symbols capitalised but are lowercase when spelt out. 'volt', 'ampere', 'coulomb', 'newton', etc. Commented Jul 31 at 18:36

To use the good old-fashioned plumbing analogy for electronics, a Coulomb of charge is exactly equivalent to a litre of water - you can deliver it slowly through a fat pipe, or quickly through a thin pipe, but it will always be one litre.

An ampere is the same - a fixed number of electrons per second - regardless of whether the wire is thin or thick, which is why it is almost the same definition as a Coulomb of charge.