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## Class 12 Physics (India)

### Course: Class 12 Physics (India)>Unit 3

Lesson 2: Electric current and voltage

# 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 $2×{10}^{-7}$ 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 $2×{10}^{-7}$ 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.
$1\phantom{\rule{0.167em}{0ex}}\text{ampere}=1\phantom{\rule{0.167em}{0ex}}\text{coulomb}/\text{second}$
or equivalently,
$1\phantom{\rule{0.167em}{0ex}}\text{coulomb}=1\phantom{\rule{0.167em}{0ex}}\text{ampere}\cdot \phantom{\rule{0.167em}{0ex}}\text{second}$

## 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 $e=-1.602176565×{10}^{-19}\phantom{\rule{0.167em}{0ex}}\text{coulomb}$.
If we invert this expression, we see that the coulomb can be stated in terms of number of electron charges:
$1\phantom{\rule{0.167em}{0ex}}\text{coulomb}=6.241509343×{10}^{18}\phantom{\rule{0.167em}{0ex}}\text{electrons}$

### Concept check

How many electrons in 1 ampere?
How many coulombs in 1 mole of electrons?
One mole of electrons is $6.02214×{10}^{23}$ 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.
$1\phantom{\rule{0.167em}{0ex}}\text{watt}=1\phantom{\rule{0.167em}{0ex}}\text{joule}/\phantom{\rule{0.167em}{0ex}}\text{second}$

## 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.
$1\phantom{\rule{0.167em}{0ex}}\text{volt}=1\phantom{\rule{0.167em}{0ex}}\text{watt}/\text{ampere}$
The volt can also be expressed in terms of energy and charge as,
$1\phantom{\rule{0.167em}{0ex}}\text{volt}=1\phantom{\rule{0.167em}{0ex}}\text{joule}/\text{coulomb}$
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.
$1\phantom{\rule{0.167em}{0ex}}\text{ohm}=1\phantom{\rule{0.167em}{0ex}}\text{volt}/\text{ampere}$
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
meter$\text{m}$length
kilogram$\text{kg}$mass
second$\text{s}$time
ampere$\text{A}$electric current
kelvin$\text{K}$temperature
candela$\text{cd}$luminous intensity
mole$\text{mol}$amount 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
coulomb$\text{C}$charge$\text{A}\cdot \text{s}$
watt$\text{W}$power$\text{J}/\text{s}$
volt$\text{V}$voltage (electric potential difference)$\text{W}/\text{A}$
ohm$\mathrm{\Omega }$resistance, impedance$\text{V}/\text{A}$
farad$\text{F}$capacitance$\text{C}/\text{V}$
henry$\text{H}$inductance$\text{Wb}/\text{A}$
hertz$\text{Hz}$frequency${\text{s}}^{-1}$
siemens$\text{S}$conductance$\text{A}/\text{V}$ or $1/\mathrm{\Omega }$
weber$\text{Wb}$magnetic flux$\text{V}\cdot \text{s}$
tesla$\text{T}$magnetic field strength$\text{Wb}/{\text{m}}^{2}$

## Want to join the conversation?

• Is it important to memorize all the units? if so, do you have any tips for memorizing them?
• I know OP is probably long gone, but for anyone else wondering no, you need not memorize it at this stage in the course. V for Volts, A for Amperes, Ω for Ohms gets you going, and will likely be hammered in.
• Do electrons require energy to flow? Or do they flow just due to the potential difference?
• 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.
• can a middle schooler study electrical engineering
• Yes. A middle schooler can get a lot from this EE subject. My curiosity about electricity started when I was about 12 years old and never stopped.
• 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?
• 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
• Is it importaint to remember all of the units?
• You should remember the most important units that we start using right away, like volts, ampere, ohm, and watt. The rest you shouldn't memorize. Just tuck away that there are lots of units and you might want to come back here some day to review them again.
• can someone please explain what
e​−=−1.602176565×10−19 coulomb
means can someone explain.
• that is the electric charge of one electron
• How do you apply "force" on the wires, as the first figure illustrates?
(1 vote)
• 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.