85 lines
2.4 KiB
ReStructuredText
85 lines
2.4 KiB
ReStructuredText
Metrics
|
|
---------------
|
|
|
|
|
|
Coulomb
|
|
^^^^^^^^^^
|
|
|
|
In a circuit, charges (electrons) flow.
|
|
This amount of charge is extremely huge.
|
|
The *Coulomb* unit allows to count them more easily.
|
|
Thus, :math:`1C \approx 6.241e^{18}` charges (electrons in our case).
|
|
|
|
Newton
|
|
^^^^^^^^^^^
|
|
It is a unit of force.
|
|
It is indirectly used in electronics (see Joule).
|
|
One Newton is the force required to accelerate :math:`1Kg` of mass, at a rate of
|
|
:math:`1m.s^{-1}` every seconds.
|
|
|
|
.. math::
|
|
[N]=kg.m.s^{-2}
|
|
|
|
Joule
|
|
^^^^^^^^^^
|
|
It is the unit of energy.
|
|
Its the force used to move an object when a force of one newton acts on that object in the direction of the force's motion through a distance
|
|
of one metre.
|
|
|
|
.. math::
|
|
[J]=[N] \times m=kg.m^2.s^{-2}
|
|
|
|
Watt
|
|
^^^^^^^
|
|
It is the amount of Joules per seconds spent by a system.
|
|
|
|
Ampere
|
|
^^^^^^^^
|
|
In a working circuit, electrons (Coulomb) are flowing.
|
|
They are flowing at a certain bitrate.
|
|
This is exactly what ampere measure.
|
|
|
|
.. math::
|
|
[A]=\frac{C}{s}=C.s^{-1}
|
|
|
|
Volt
|
|
^^^^^^^
|
|
To move charges in a circuit, energy is required (energy that push the charges).
|
|
This is what volts measure.
|
|
A volt is the amount of energy per Coulomb (remember Coulomb
|
|
is just a constant).
|
|
|
|
.. math::
|
|
[V]=\frac{[J]}{C}=kg.m^2.s^{-2}.C^{-1}=kg.m^2.s^{-3}.C^{-1}.s=kg.m^2.s^{-3}.[A]^{-1}
|
|
|
|
Farad
|
|
^^^^^^^^
|
|
Components can hold electrons (such as capacitor).
|
|
Farad defines the amount of Coulomb (electrons) retained by the component for each unit of voltage.
|
|
|
|
.. math::
|
|
{[F]}=\frac{C}{[V]}=\frac{C}{kg.m^2.s^{-3}.[A]^{-1}}&=\frac{C}{kg.m^2.s^{-3}.C^{-1}.s}=\frac{C}{kg.m^2.s^{-2}.C^{-1}}
|
|
|
|
&=\frac{C^2}{[J]} =\frac{C^2}{[N].m} =\frac{s^2.C^2}{kg.m}
|
|
|
|
&=\frac{s^4.[A]^2}{kg.m}=m^{-2}.kg^{-1}.s^4.[A]^2
|
|
|
|
Ohm
|
|
^^^^^^^
|
|
In circuits, components can resist to the current and thus reduces it.
|
|
Ohm defines the amount of volts required at one end of the resistor to pass one ampere into it.
|
|
|
|
.. math::
|
|
{[\Omega]}=\frac{[V]}{[A]}=\frac{kg.m^2.s^{-3}.[A]^{-1}}{[A]}=kg.m^2.s^{-3}.[A]^{-2}&=kg.m^2.s^{-3}.C^{-2}.s^{2}
|
|
|
|
&=kg.m^2.s^{-1}.C^{-2}
|
|
|
|
Henry
|
|
^^^^^^^^^^
|
|
An inductor is resisting to change in current.
|
|
When current is changing, a voltage appears at the inductor terminals.
|
|
Henry corresponds to the voltage measurable across the inductor terminals when the current is changing at a rate of one ampere per second.
|
|
|
|
|
|
.. math::
|
|
H=\Omega.s=\frac{kg.m^2.s^{-3}.[A]^{-1}}{[A]} \times s = \frac{m^2.kg}{s^2.[A]^2} = m^2.kg.s^{-2}.[A]^{-2}
|