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