Generator Constants: Understanding RLC Circuits in Series and Parallel

[Jhenrique]

If in a typical complete circuit (RLC) we have a resistor with resistence R, an inductor with inductance L and a capacitor with capacitance C, so the generator has which constants?

And in second place, I was searching about the math of generators in series and parallel and I found something only here:
http://es.wikipedia.org/wiki/Circuito_en_serie
http://es.wikipedia.org/wiki/Circuito_en_paralelo

The equations for $V$ and $I$ are true?

 

[Simon Bridge]

If you want to know how RCL circuits combine, you want to look up the theory of 2-terminal networks.
I don't know what you mean by the constants of a generator.

The equations on those pages are correct for ideal components.

 

[Jhenrique]

The equations on those pages are correct for ideal components.

By "generator" I'm thinking in a battery! Is obvius that every battery has a voltage as constant, but still so I asked for see what kind of answer I would have... anyway, a (ideal) battery has amperage too? If yes, so why the amperage never is specified? If no, so how I can to discovered the amperage of a system with a battery?

 

[Simon Bridge]

Oh you mean a voltage source?!
By "amperage" I guess you mean "current"?

An ideal voltage source has a fixed voltage-amplitude and frequency.
An ideal current source has a fixed current-amplitude and frequency.

An ideal DC voltage source would have a frequency of zero.

A real voltage source is modeled by an ideal voltage source in series with a small resistance.

A battery would be a real DC voltage source - but the engineering means you have to be careful about combining them in a real circuit.

Ideal voltage sources have the property that the voltage is the same no matter what they are connected to, though the circuit may draw varying amounts of current. This is why a current is never specified: ideal sources can supply any current that is asked of them. Real voltage sources will get hot when they are over-worked and may break down or explode.

A maximum current is usually specified, or some sort of "normal use" is indicated, on the packaging.
Real life constant-voltage PSUs are usually equipped with some sort of current limitation device.

You can calculate the current through any component connected to a voltage source from Ohm's Law... in LRC circuits you need to use the impedence instead of resistances.

 

[Jhenrique]

The voltage and current respect the following equations:

Source: http://es.wikipedia.org/wiki/Circuito_en_serie2) And for some generators associated in parallel:

The voltage and current respect the following equations:

Source: http://es.wikipedia.org/wiki/Circuito_paralelo

But how I'll make the sum of the currents for get the total current in a parallel circuit if I don't know the value of the current of each generator!?*

And how I'll say that the current of my system of generators is equal to x amperes if I don't know the value of the current of none generator!?*

*'cause each generator has a voltage $Vi$ specified but haven't the current $Ii$ specified.

 

[Simon Bridge]

Please understand, in post #4 I was giving you a bunch of definitions so you can express yourself better.

In English, an electric "generator" is a particular kind of machine.
Please do not say "generator" unless you mean something involving magnets and coils and moving parts.

The proper word for the electric component in a circuit diagram that you are talking about is "voltage source".

In post #5. there are four diagrams shown.
The top two diagrams contain ideal DC voltage sources.
The lower diagrams are all ideal AC voltage sources.

Currents:
In the top two diagrams, the currents are calculated using kirchhoffs laws.

This will work for the other diagrams too, but we don't need to: there's a short cut.
In the diagram where all the voltage sources are in series, the currents are all zero. This is because there is no circuit - without a circuit no current can flow.
In the diagram where they are all in parallel - also zero, because there are no potential differences except across the sources. With no potential difference, there can be no current.

You seem to think there must be a current associated with a voltage source just like there is a voltage associated with it. This is not the case. The current flowing through (into and out of) a voltage source depends on what it is connected to. It is not a property of the voltage source.

 

[Jhenrique]

You seem to think there must be a current associated with a voltage source just like there is a voltage associated with it. This is not the case. The current flowing through (into and out of) a voltage source depends on what it is connected to. It is not a property of the voltage source.

Point of view very interesting for me!

If the resistance is a property of the resistor, the inductance of the inductor, the capacitance of the capacitor and the voltage of the voltage source, so the current is a property of which electrical element?

 

[Simon Bridge]

Point of view very interesting for me!

If the resistance is a property of the resistor, the inductance of the inductor, the capacitance of the capacitor and the voltage of the voltage source, so the current is a property of which electrical element?

Following that scheme, it is the property of a component called a "current source".
An ideal current source has a current but no set voltage - the voltage across the current source is determined by what it is connected to.

But more properly, voltage is not a property restricted to voltage sources, but of electric fields. Similarly current is the motion of charges when they are influenced by electric fields.

 

[Jhenrique]

Hummm... so in a circuit with a resistor of resistance R, an inductor of inductance L, a capacitor of capacitance C and a voltage source of voltage V, the current I is not predetermined for none device, so the current is an unknown variable and is function of R, L, C and V. Correct?

Similarly, in a circuit with a resistor of resistance R, an inductor of inductance L, a capacitor of capacitance C and a current source of current I, the voltage V is not predetermined for none device, so the voltage is an unkown variable and is function of R, L, C and I. Correct?

 

[Windadct]

I think you have it, I am assuming that when you say "for none device" you mean "I is not predetermined for any device in the circuit"?

Again keep in mind all of this is referring to IDEAL models - one of the great things about electrical circuits is that within normal operating ranges, they behave very close to the ideal - however all real devices have limits where these behaviors are close to the ideal model, outside of which other factors come into play ( a conductor can only carry so much current until it's own finite resistance causes heating which changes (typically increasing) it's resistance).

 

[Simon Bridge]

Hummm... so in a circuit with a resistor of resistance R, an inductor of inductance L, a capacitor of capacitance C and a voltage source of voltage V, the current I is not predetermined for none device, so the current is an unknown variable and is function of R, L, C and V. Correct?

Similarly, in a circuit with a resistor of resistance R, an inductor of inductance L, a capacitor of capacitance C and a current source of current I, the voltage V is not predetermined for none device, so the voltage is an unknown variable and is function of R, L, C and I. Correct?

As Windadct writes - both statements look to be correct. Don't forget that voltages and currents can, and usually do, vary around the circuit no matter which source is used.

A circuit may include both voltage and current sources. Sources may be placed anywhere in the circuit - they do not have to appear in easy combinations like your examples. The voltage and current for the other components in the circuit are calculated from Kirchoff's laws.

 

[Jhenrique]

As Windadct writes - both statements look to be correct. Don't forget that voltages and currents can, and usually do, vary around the circuit no matter which source is used.

It's make sense, cause if you has a dynamical circuit with 5 paramaters, R, L, C, V and I, where R, L, C and V are constants, at least one parameter needs be variable, the current I, otherwise it isn't a dynamical system and but yes a statical system.

A circuit may include both voltage and current sources. Sources may be placed anywhere in the circuit - they do not have to appear in easy combinations like your examples. The voltage and current for the other components in the circuit are calculated from Kirchoff's laws.

What? Can exist one RLC circuit with voltage source and with current source too? I think that or the voltage needs be free or a current needs be free, a circuit with current source and voltage source imposes constraints in the voltage and current, correct?

 

[Simon Bridge]

If you specify too much the problem becomes "over-specified" and the situation may be physically impossible.
A bit like in mechanics, if you specify the force, the mass, and the acceleration, instead of just two of them.
If you insist that a voltage source is providing 1.5V and 2mA and it is series with a 1Ohm resistor you have an impossible situation.

Voltage and current sources only set the voltage and current close to them, not for the whole circuit.
So it is perfectly OK to have them both in the same circuit.
Consider:

... what is the voltage across the 1200 Ohm resistor?

 

[Jhenrique]

If you specify too much the problem becomes "over-specified" and the situation may be physically impossible.
A bit like in mechanics, if you specify the force, the mass, and the acceleration, instead of just two of them.
If you insist that a voltage source is providing 1.5V and 2mA and it is series with a 1Ohm resistor you have an impossible situation.

Voltage and current sources only set the voltage and current close to them, not for the whole circuit.
So it is perfectly OK to have them both in the same circuit.
Consider:

I don't understand, your two paragraphs above are contradictory... in the 1st you says that very information can turn the system impossible. In the second you says that it isn't impossible...

... what is the voltage across the 1200 Ohm resistor?

1.9V, I think...

 

[Simon Bridge]

I don't understand, your two paragraphs above are contradictory... in the 1st you says that very information can turn the system impossible. In the second you says that it isn't impossible...

In the first I am talking about specifying the voltage and the current for the same source and in the second I am talking about having voltage and current sources in the same circuit. The example circuit illustrates how this is not fatal.

1.9V, I think...

... well done: so you are saying that you can see how it is OK to have voltage and current sources in the same circuit?

Notice how the voltage and the current in each part of the circuit depends on all the components?
Notice how the voltage is not specified for the current source and the current is not specified for the voltage source?
If I had specified that the voltage source is putting out 1mA of current at the start - is that possible?

 

[Jhenrique]

Notice how the voltage and the current in each part of the circuit depends on all the components?

Yes!

Notice how the voltage is not specified for the current source and the current is not specified for the voltage source?

Yes!

If I had specified that the voltage source is putting out 1mA of current at the start - is that possible?

No!

 

[Simon Bridge]

And there you have it. All clear now?

 

[Jhenrique]

And there you have it. All clear now?

Yeah!

 

[Simon Bridge]

Outstanding! Enjoy ;)