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Defining the standard electrical units

Formal definitions of the standard electrical units: ampere, coulomb, charge on an electron, and the volt. Written by Willy McAllister.
Electrical units can be described in a formal manner, and that's what we do here. The standard electrical units are defined in a specific order. The ampere is defined first. It is an SI base unit, the only electrical unit derived from the outcome of an experiment.
Next up after the ampere comes the coulomb and charge on an electron. Then we derive the rest of our favorites, the watt, the volt, and the ohm. These derived electrical units are defined in terms of the ampere and other SI base units (meter, kilogram, second).

Ampere

The definition of the SI unit of current, the ampere, comes from the study of magnetism. Electric currents in wires give rise to magnetic fields (Biot–Savart Law, 1820). Those magnetic fields in turn give rise to magnetic forces on the wires (Ampere's Force Law, 1825). Two parallel wires carrying current exert a force on each other. The official SI definition of the ampere is:
The ampere is that constant current which—if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum—would produce between these conductors a force equal to 2, times, 10, start superscript, minus, 7, end superscript newtons per meter of length.
The definition of the ampere comes from the outcome of an experiment. To create a standard 1 ampere, you perform some version of the following experiment. Set up two 1-meter-long wires in parallel, and arrange for a way to measure the force on the wires (a strain gauge).
Apply the same current to both wires, flowing in the same direction. Adjust the currents in the wires up or down while measuring the force on the wires. When the force is 2, times, 10, start superscript, minus, 7, end superscript newtons, the current is 1 ampere, by definition. (This is a conceptual experiment. In modern standards laboratories a standard ampere is created by other means.)

Coulomb

The coulomb is the SI unit of charge. The size of a coulomb is derived from the ampere. One coulomb is defined as the amount of charge flowing when the current is 1 ampere.
1, start text, a, m, p, e, r, e, end text, equals, 1, start text, c, o, u, l, o, m, b, end text, slash, start text, s, e, c, o, n, d, end text
or equivalently,
1, start text, c, o, u, l, o, m, b, end text, equals, 1, start text, a, m, p, e, r, e, end text, dot, start text, s, e, c, o, n, d, end text

Electron charge

In 1897, J.J. Thomson proved the existence of the electron. Twelve years later, starting in 1909, Robert Millikan performed his oil drop experiments to establish the charge of the electron.
The charge on an electron can be expressed in coulombs as e, equals, minus, 1, point, 602176565, times, 10, start superscript, minus, 19, end superscript, start text, c, o, u, l, o, m, b, end text.
If we invert this expression, we see that the coulomb can be stated in terms of number of electron charges:
1, start text, c, o, u, l, o, m, b, end text, equals, 6, point, 241509343, times, 10, start superscript, 18, end superscript, start text, e, l, e, c, t, r, o, n, s, end text

Concept check

How many electrons in 1 ampere?
How many coulombs in 1 mole of electrons?
One mole of electrons is 6, point, 02214, times, 10, start superscript, 23, end superscript electrons — Avogadro's Number.

Watt

The watt is the unit of power. Power is the amount of energy transferred or consumed per unit of time; equivalently, power is the rate of doing work. In standard-speak, the watt is the power which in one second gives rise to energy of 1 joule.
1, start text, w, a, t, t, end text, equals, 1, start text, j, o, u, l, e, end text, slash, start text, s, e, c, o, n, d, end text

Volt

The volt is the unit of electric potential difference—electric potential difference is also known as voltage. The size of 1 volt is officially defined as the potential difference between two points of a wire carrying a current of 1 ampere when the power dissipated in the wire is 1 watt.
1, start text, v, o, l, t, end text, equals, 1, start text, w, a, t, t, end text, slash, start text, a, m, p, e, r, e, end text
The volt can also be expressed in terms of energy and charge as,
1, start text, v, o, l, t, end text, equals, 1, start text, j, o, u, l, e, end text, slash, start text, c, o, u, l, o, m, b, end text
You can find an intuitive description of voltage in the introductory article on basic electrical quantities. Also, there is a formal derivation of the meaning of voltage in the electrostatics section.

Ohm

The ohm is the electrical unit of resistance. One ohm is defined as the resistance between two points of a conductor when 1 volt is applied and a current of 1 ampere is flowing.
1, start text, o, h, m, end text, equals, 1, start text, v, o, l, t, end text, slash, start text, a, m, p, e, r, e, end text
We've now defined, in order, a basic set of our favorite electrical units.

Systems of Units

Over the last 200 years, there have been three main systems of scientific units:
  • SI
  • MKS
  • cgs
SI is the International System of Units—in French, Système International d'Unités. It is the modern form of the metric system and is the most widely used system of measurement. The system was published in 1960 as the result of discussions that started in 1948. SI is based on the metre-kilogram-second system (MKS). In the United States, the SI is used in science, medicine, government, technology, and engineering.
MKS is based on measuring lengths in meters, mass in kilograms, and time in seconds. MKS is generally used in engineering and beginning physics. It was proposed in 1901. The most familiar units of electricity and magnetism—ohm, farad, coulomb, etc.—are MKS units.
cgs is based on measuring lengths in centimeters, mass in grams, and time in seconds. It was introduced in 1874. The cgs system is commonly used in theoretical physics. The difference between the SI and cgs systems goes much deeper than a simple scaling of the units for length and mass.
There are seven SI base units.

SI base units

NameSymbolQuantity
meterstart text, m, end textlength
kilogramstart text, k, g, end textmass
secondstart text, s, end texttime
amperestart text, A, end textelectric current
kelvinstart text, K, end texttemperature
candelastart text, c, d, end textluminous intensity
molestart text, m, o, l, end textamount of substance
One SI base unit comes from electricity: the ampere. The ampere has the same lofty status as the meter, kilogram, and second. It is defined as its own thing, not in terms of other units.

SI derived units used in electricity

The remaining electrical units are SI derived units, formed by combinations of the base units. If the ampere is the "first" electrical unit, these derived electrical units follow close behind.
NameSymbolQuantityIn terms of other SI units
coulombstart text, C, end textchargestart text, A, end text, dot, start text, s, end text
wattstart text, W, end textpowerstart text, J, end text, slash, start text, s, end text
voltstart text, V, end textvoltage (electric potential difference)start text, W, end text, slash, start text, A, end text
ohm\Omegaresistance, impedancestart text, V, end text, slash, start text, A, end text
faradstart text, F, end textcapacitancestart text, C, end text, slash, start text, V, end text
henrystart text, H, end textinductancestart text, W, b, end text, slash, start text, A, end text
hertzstart text, H, z, end textfrequencystart text, s, end text, start superscript, minus, 1, end superscript
siemensstart text, S, end textconductancestart text, A, end text, slash, start text, V, end text or 1, slash, \Omega
weberstart text, W, b, end textmagnetic fluxstart text, V, end text, dot, start text, s, end text
teslastart text, T, end textmagnetic field strengthstart text, W, b, end text, slash, start text, m, end text, squared

Want to join the conversation?

  • female robot ada style avatar for user Sanyarora
    Is it important to memorize all the units? if so, do you have any tips for memorizing them?
    (31 votes)
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  • piceratops ultimate style avatar for user Manan Jain
    Do electrons require energy to flow? Or do they flow just due to the potential difference?
    (9 votes)
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    • blobby green style avatar for user D B Brumm
      If there is a potential difference, then energy is imparted to the electrons by the electric field. Compare it to a mass under the influence of gravity. The gravitational field must impart energy to the mass before it moves. Similarly the electric field imparts energy to electrons, making them move.
      (26 votes)
  • duskpin sapling style avatar for user Mansour
    can a middle schooler study electrical engineering
    (4 votes)
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  • leaf green style avatar for user Shaw Olsen
    Regarding the first concept check: How many electrons in 1 ampere?

    Does it make sense to try to think of some amount of electrons being equivalent to an ampere? If I understand it right an ampere is a really not a thing, but a rate (things per second)...so isn't this kind of like asking how many inches are in 1 mile per hour?
    (3 votes)
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    • spunky sam orange style avatar for user Willy McAllister
      Electric current is kind of like water current. When we talk about water current we treat the water as a continuous fluid, not as a collection of water molecules. We have units for current like gallons per minute or liters per second. You pretty much never measure current in molecules/second.

      If we treat electric current like it is a fluid the current measurements are analogous. Instead of gallons or liters, we measure charge in coulombs. A coulomb is an amount of charge. Current is a rate, so it measures coulombs/second. A current of 1 coulomb/sec has an honorary name, the ampere.

      Long after people knew about electric current and were happy measuring it in C/sec = A, someone came along and discovered the electron. Current in wires is actually the flow of electrons. There are about 6 x 10^18 electrons in a coulomb. One ampere is 6 x 10^18 electrons per second.

      Check out this complete answer... https://spinningnumbers.org/a/charge.html#measuring-charge-by-counting-electrons
      (6 votes)
  • male robot donald style avatar for user Masen Storms
    Is it importaint to remember all of the units?
    (3 votes)
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  • leafers ultimate style avatar for user diego.luna
    can someone please explain what
    e​−=−1.602176565×10−19 coulomb
    means can someone explain.
    (0 votes)
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  • leaf blue style avatar for user Gavin
    How do you apply "force" on the wires, as the first figure illustrates?
    (1 vote)
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    • spunky sam orange style avatar for user Willy McAllister
      The force on the wires comes from the current flowing in the wires. The current in each wire generates a magnetic field in the space around the wire. The magnetic fields from the two wires overlap and generate a force, just like if you bring two bar magnets near each other. To do the experiment you measure the force (with a strain gauge, for example). Then you adjust the current in the wires until the measured force is a certain value. At that point, the current in the wires is 1 ampere, by definition.
      (7 votes)
  • blobby green style avatar for user Gregory Phillips
    can someone please explain ampere better I didn't really understand that so much. It would be really appreciated.
    (3 votes)
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  • ohnoes default style avatar for user h_cartwright
    Is the telsa car comany named after the tesla magnetic field strength? The symbol is the same as tesla's logo
    (2 votes)
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  • piceratops seedling style avatar for user Islam Hamed
    What is the difference between energy and work?
    (3 votes)
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    • purple pi purple style avatar for user APDahlen
      Hello Semsempequrest,

      You could call them the same thing. We could say that a pile of coal contains X units of energy. We could also say that the same pile of coal is capable of performing X units of work.

      A related question is how does energy relate to power. I've been experimenting on YouTube to answer these questions. Please take a look at this video and let me know what you think:

      https://www.youtube.com/watch?v=EQxCkq4BFKQ

      Regards,

      APD
      (1 vote)