Electricity is electrons – the negative charge which orbits around the nucleus of an atom.

Coulomb

The Coulomb is the measure of the quantity of electrons. Just as litres or gallons is used to measure the quantity of a liquid, Coulombs is used to measure the quantity of electrons.

A Coulomb contains approximately 6.24 × 10¹⁸ electrons.

A Coulomb is defined as:

The symbol for the Coulomb is the upper case letter C.

It is derived from the basic SI units of ampere and second.

Ampere

The ampere (often shortened to amp) is the measure of the flow of electrons. Just as litres per second or gallons per second is used to measure the flow of a liquid, Amperes is used to measure the flow of electrons.

It is equal to the constant flow of one Coulomb of charge over one second.

A = C / s

The official SI definition is:

The symbol for the Ampere is the upper case letter A.

This is a fundamental or basic SI unit.

Volt

The volt is the measure of the electromotive force (e.m.f), electrical pressure, or “push” that moves electrons from one place to another. Just as Pascals or pounds per square inch are used to measure the pressure exerted by a liquid, Volt is used to measure the electrical pressure.

The Volt is defined as:

The volt used to be defined as:

The symbol for the Volt is the upper case letter V.

It is derived from the basic SI units of Ampere and the derived SI unit of Watt.

Ohm

The Ohm is the measure of a material’s resistance to the flow of electrons.

The Ohm is defined as

The symbol for the Ohm is the upper case Greek letter Omega: Ω.

The ohm used to be defined as:

It is derived from the basic SI unit Ampere and the derived SI unit Volt.

Watt

The Watt is the measure of power.

The electrical Watt is defined as

The symbol for the Watt is the upper case letter W.

It is derived from the basic SI unit second and the derived SI unit of Joule.

Difference Between Amperes and Volts

Amperes is the rate at which electricity is flowing in the circuit, while volts is the pressure that causes the electricity to flow.

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In mathematics:

• Unknown things are often written using x, y, or z.
• Known things are often written using a, b, or c.
• Functions are often written using f, g, or h.

A function is an abstraction. Just as using a variable lets you talk about an unknown value in an equation:

x² + 2 = 6

x²+ y = 7

using a function lets you generalize about mathematical operations:

f(x)
g(x, y)

The actual mathematical operation doesn’t matter because all functions have certain properties and behaviours in common. Besides, it is a lot easier to write f(x) than some long equation.

In mathematical terms:

This simply means that a function

• takes things found in A (the domain)
• does something to them
• and returns things found in B (the codomain)

There is no restriction on what sets A and B are. They could be

• a set of integers,
• a set of real numbers
• a set of functions returning positive integers
• a set of convex polygons
• a set of two dimensional data representing images

They don’t even have to be the same sets – the codomain can be different from the domain.

The only restriction is that there can only be one mapping from A to B. In other words, every single item in the set A, when processed by the function, can only map to a single item from the set B. Although, multiple items in A can map to the same item in B.

For example, given

f(x) = √x

• If the domain is the set of positive real numbers (i.e. all numbers greater than 0) and if the codomain is the set of all positive real numbers, then f(x) is a function.
• If the domain is the set of positive real numbers and if the codomain is the set of all real numbers (both positive and negative), then f(x) is not a function (hint, √4 can be 2 or –2).

If we are given

f(x) = x – x

then no matter what the domain is, the codomain is always the set containing 0. Therefore, every element in the domain (set A) maps to exactly one element in the codomain (set B). They just all happen to map to the same element.

Given this restriction, our mathematical definition now looks like this:

Notation

Functions can be referred to by just a letter – f being the most common.

You can have a whole bunch of functions and refer to them as f₁, f₂, f₃, … f_n.

Functions can be written with parameters – f(x) being common. It should be read as “the value of x being evaluated / processed by the function f”.

Functions can have a whole bunch of parameters:

f(x, y)

f(x, y, z, w)

f(x₁, x₂, … x_n)

The function can be defined for you:

f(x) = x² + 3x + 2

It can also be defined in terms of other functions:

g(x, y) = ∫∫f(x,y)

(Here, g(x, y) is being defined as the double integration of function f(x, y))

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