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mcastillo356
Gold Member
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Hi, PF, this thread is meant to be an introduction to the principles of ##DC## and ##AC##, but I'm very much insecure about the rigurosity of my point of view, so I prefer to post at the lounge. There it goes: fasten seat belts 
The textbook ("Pre-university Physics Principles", by the UNED: State Distance University, translated from Spanish to English) is some chapters selection based on "Essential College Physics", by Andrew Rex and Richard Wolfson...
The coulomb is defined by means of the ampere; this last is the unit of electrical current.
Introduction to electrical current
Electrical current is a flow of electrical charge, the rate at which it runs by any given point. More precisely:
$$I=\displaystyle\frac{\Delta q}{\Delta t}$$
This is, electrical current; IS units: ##A##
Electrons flow and positive charge
The above equation means that the current flows in the direction of the movement of the positive charges (no clue about why, anyhow, attempt: electrical current, I mean, the rate above, is always positive, and therefore both ##\Delta q## and ##\Delta t## - this last obviously - are positive)
Nevertheless, in most of the electrical circuits, it is the negative electrons at the conductor cables those to carry the current. By convention, we keep expressing the current direction as if they were positive charges the ones to move, but in the opposite direction to the negative electrons. This avoids negative aditional simbols whenever studying circuits.
We have seen in the previous chapter that positive charges move from spots of more electrical potential to lesser. In a circuit, this means we can understand current as if it would flow from the positive terminal of the battery to the negative one, travelling around all the circuit. It is the same current (from positive to negative), regardless of wether it is eventually positive charges from batery's positive to negative terminal, or negative electrons going from negative to positive terminal. If this sounds confusing,... Blame it on Ben Franklin for choosing the term "negative" for the charge we now know is related to electrons! (sic)
. When the current flows in only one direction we call it direct current, or DC. In the next chapter we will study the alternating current, AC, which reverses periodically.
Electromotive force and inner resistance
In the previous chapter, we've described batteries as devices that provide a constant electric potential difference. It is common to refer to them as a source of electromotive force, or emf. This terminology is obsolete and leads to confusion, because there is only an indirect relationship indeed with the concept of force in physics. A battery emf is the electric potential amount in its cell or cells, like for example 1.5 ##V## in a lantern battery. Emf is designed by the symbol ##\mathcal{E}##, to distingish from other potential differences that are not concerned with electrical energy sources. While those other potential differences can change depending on the circumstances of some certain circuit, the emf ##\mathcal{E}## of a battery is ideally fixed, due to its chemical nature. (I personally think that the texbook I own is fuzzy; these last two written sentences, for example, make allusion to other potential differences aside from electricity, but in the end seems to make a mess of all kind of potential differences).
When we conect a battery to a fully equipped circuit, the current flows throughout it. The circuit external to the battery is the electrical load, ie, a bulb light or whatever electrical implement we wish to connect. On ideal batteries the electrical potential amount between the terminals is just the emf of the battery and is free from the charge (what mean these five previous words?), despite the battery inner resistance.
(...)
Electromagnetic induction and alternating current
In the previous chapter we have seen that electric and magnetic events are closely related. Electric currents lead to the appearance of magnetic fields, while magnetic fields in turn affect moving electric charges. Based on these so close link, it is reasonable to ask another question: if the electric current creates a magnetic field, could a magnetic field provide an electric current? The answer is yes, and this fact is called electromagnetic induction.
Generators and transformers
The induction plays a key role in the electrical energy supply sistems. In this section we will see how is precisely the electrical induction phenomenon which allows us to generate almost all of the electricity we consume, as well as converting potential differences, thus allowing the transmission of electricity over long distances.
(...) How does an electric generator work? We know from Faraday's law, that the induced current requires a variable magnetic flow. With a uniform field, we have the equation ##\Phi=BA\cos{\theta}## for the flow that goes through each turn of a coil (a moving magnet induces a current in a coil ) The magnetic field ##B## and the area ##A## are constant, but as the coil turns, the angle ##\theta## changes. If the coil goes round with a constant angular speed ##\omega##, then we know from a previous chapter that ##\theta=\omega\,t##. Thus, by Faraday's law, the emf will be
$$\mathcal{E}=-N\displaystyle\frac{\Delta\Phi}{\Delta{t}}=-N\displaystyle\frac{\Delta{(BA\cos{\theta})}}{\Delta{t}}=-NBA\displaystyle\frac{\Delta{(\cos{(\omega\,t)})}}{\Delta{t}}$$
for a coil of ##N## turns. Applying calculus tools, we deduce that the above formula leads to a instantaneous value
$$\mathcal{E}=NBA\omega\cos{(\omega\,t)}$$
Thus, the induced emf changes sinusoidally with time, periodically turning from positive to negative values. This renders an alternating current, which switches direction regularly. The electric supply travels through power lines to houses and offices.
How does it look this electrical digest?
PD: Post without preview.
The textbook ("Pre-university Physics Principles", by the UNED: State Distance University, translated from Spanish to English) is some chapters selection based on "Essential College Physics", by Andrew Rex and Richard Wolfson...
The coulomb is defined by means of the ampere; this last is the unit of electrical current.
Introduction to electrical current
Electrical current is a flow of electrical charge, the rate at which it runs by any given point. More precisely:
$$I=\displaystyle\frac{\Delta q}{\Delta t}$$
This is, electrical current; IS units: ##A##
Electrons flow and positive charge
The above equation means that the current flows in the direction of the movement of the positive charges (no clue about why, anyhow, attempt: electrical current, I mean, the rate above, is always positive, and therefore both ##\Delta q## and ##\Delta t## - this last obviously - are positive)
Nevertheless, in most of the electrical circuits, it is the negative electrons at the conductor cables those to carry the current. By convention, we keep expressing the current direction as if they were positive charges the ones to move, but in the opposite direction to the negative electrons. This avoids negative aditional simbols whenever studying circuits.
We have seen in the previous chapter that positive charges move from spots of more electrical potential to lesser. In a circuit, this means we can understand current as if it would flow from the positive terminal of the battery to the negative one, travelling around all the circuit. It is the same current (from positive to negative), regardless of wether it is eventually positive charges from batery's positive to negative terminal, or negative electrons going from negative to positive terminal. If this sounds confusing,... Blame it on Ben Franklin for choosing the term "negative" for the charge we now know is related to electrons! (sic)
. When the current flows in only one direction we call it direct current, or DC. In the next chapter we will study the alternating current, AC, which reverses periodically.Electromotive force and inner resistance
In the previous chapter, we've described batteries as devices that provide a constant electric potential difference. It is common to refer to them as a source of electromotive force, or emf. This terminology is obsolete and leads to confusion, because there is only an indirect relationship indeed with the concept of force in physics. A battery emf is the electric potential amount in its cell or cells, like for example 1.5 ##V## in a lantern battery. Emf is designed by the symbol ##\mathcal{E}##, to distingish from other potential differences that are not concerned with electrical energy sources. While those other potential differences can change depending on the circumstances of some certain circuit, the emf ##\mathcal{E}## of a battery is ideally fixed, due to its chemical nature. (I personally think that the texbook I own is fuzzy; these last two written sentences, for example, make allusion to other potential differences aside from electricity, but in the end seems to make a mess of all kind of potential differences).
When we conect a battery to a fully equipped circuit, the current flows throughout it. The circuit external to the battery is the electrical load, ie, a bulb light or whatever electrical implement we wish to connect. On ideal batteries the electrical potential amount between the terminals is just the emf of the battery and is free from the charge (what mean these five previous words?), despite the battery inner resistance.
(...)
Electromagnetic induction and alternating current
In the previous chapter we have seen that electric and magnetic events are closely related. Electric currents lead to the appearance of magnetic fields, while magnetic fields in turn affect moving electric charges. Based on these so close link, it is reasonable to ask another question: if the electric current creates a magnetic field, could a magnetic field provide an electric current? The answer is yes, and this fact is called electromagnetic induction.
Generators and transformers
The induction plays a key role in the electrical energy supply sistems. In this section we will see how is precisely the electrical induction phenomenon which allows us to generate almost all of the electricity we consume, as well as converting potential differences, thus allowing the transmission of electricity over long distances.
(...) How does an electric generator work? We know from Faraday's law, that the induced current requires a variable magnetic flow. With a uniform field, we have the equation ##\Phi=BA\cos{\theta}## for the flow that goes through each turn of a coil (a moving magnet induces a current in a coil ) The magnetic field ##B## and the area ##A## are constant, but as the coil turns, the angle ##\theta## changes. If the coil goes round with a constant angular speed ##\omega##, then we know from a previous chapter that ##\theta=\omega\,t##. Thus, by Faraday's law, the emf will be
$$\mathcal{E}=-N\displaystyle\frac{\Delta\Phi}{\Delta{t}}=-N\displaystyle\frac{\Delta{(BA\cos{\theta})}}{\Delta{t}}=-NBA\displaystyle\frac{\Delta{(\cos{(\omega\,t)})}}{\Delta{t}}$$
for a coil of ##N## turns. Applying calculus tools, we deduce that the above formula leads to a instantaneous value
$$\mathcal{E}=NBA\omega\cos{(\omega\,t)}$$
Thus, the induced emf changes sinusoidally with time, periodically turning from positive to negative values. This renders an alternating current, which switches direction regularly. The electric supply travels through power lines to houses and offices.
How does it look this electrical digest?
PD: Post without preview.
