Capacitor vs Inductor

[Tahmeed]

HI, can anyone share a very clear idea with me?......
 about...
1. What is the actual meaning of leading or lagging of voltage or current in an inductor or in a capacitor?
2. At transient condition actually what happens inside of an inductor or a capacitor?
3. How transient state turns into a steady state?

simulating with multisim (version 10.0) i've got two brain cracking curves ... please someone help me with these weird curves....

[tedz]

Well, let's look at the basics, in a very simplified way:

- A capacitor stores a charge, which then presents itself to the outside as a voltage over its terminals. To change that charge/voltage, one has to supply a current to the capacitor (discharging is also by a current, but it flows the opposite way). If the capacitor is ideal (no leakage!), the current is zero, when the voltage is constant.

- An inductor stores a magnetic field, which then presents itself to the outside as current flowing through the inductor. You can "charge" an inductor by supplying a voltage over it. If the inductor is ideal (no series resistance), the voltage is zero, when the current is constant.

- In other words, both components store energy. To fill the store, you have to put energy in, and then you may afterward recover it - "take it out"

- The storage also represents a tendency of resisting a change in the energy state. This tendency causes the lagging phenomena on the "primary" type of electrical stimulus (voltage or current), and "leading" on the secondary (current or voltage). What is primary and what is secondary is opposite for a capacitor and an inductor, as capacitor stores voltage, inductor stores current.

Let's look for example the capacitor. Let's start from a discharged state - thus the voltage across its terminals is zero. If we now connect a generator to the capacitor, and let the initial voltage of it to be zero, nothing happens. No current, zero voltage. We also assume, that there is a resistance in series with the ideal voltage source generator. You see soon why (also, no real generator can have zero internal resistance!)

However, if our generator now starts to deliver a voltage, there will be current through the resistor, and to the capacitor. For simplicity, we can use a step voltage. The capacitor is now charging, and its voltage is rising. The magnitude of current going into it is defined by (generator's voltage - capacitor's voltage) / resistance.

Now we see, that the voltage over capacitor is "lagging" the generator voltage = follows it with delay. But the current is first high, then reducing (="leading"). (Similar relation will show with sine-wave input, but in that case we have a "moving target-voltage")

If we do the same with an inductor, the behavior of voltage and current are reversed: Inductor current is first zero, and then increases over time (is "lagging"), while the voltage is "leading"

A transient is just a momentary state of things. You insert the values of circuitry, and calculate the momentary voltage and current from the values. Just remember, that capacitor does not want to change its voltage in infinitesimal small time, and inductor doesn't want o change its current in zero time.

Steady state is actually never 100% achievable, but given enough time, we are reaching something, which we call "steady state". For instance, in the simple case of charging a capacitor through a resistor, the steady state is when the resistor's current is virtually zero, and capacitor's voltage in practice equal to generator's (=the difference is very, very small)

I hope this answers at least part of your questions.

.tedz

[hate]

Steady state is actually never 100% achievable, but given enough time, we are reaching something, which we call "steady state". For instance, in the simple case of charging a capacitor through a resistor, the steady state is when the resistor's current is virtually zero, and capacitor's voltage in practice equal to generator's (=the difference is very, very small)

Actually steady state is 100% achievable when the capacitor current decrease under 1.602176487exp(−19) C/s or so. That's less than 1 electron/second and u can't feed the capacitor less than 1 electron so it's steady state. But before it comes to this there are lots of effects in real life like electromagnetic radiation which effects current. Considering the exponential relationship between current and voltage in a STC (Single Time Constant) network, u can consider the system is in a steady state after 5 Time Constants. The Time Constant of a STC network is the inverse of the Capacitance times Resistance. Also an STC network is for example a resistor and a capacitor tied to a voltage source in series.

Regards...

[Tahmeed]

@tedz n hate....
thanx to u all buddy......
your infos really helped.......
but thinking of 1 thing...........
 if somehow we get an ideal 0 resistance generator
 then will there be no leading or lagging???

[solutions]

Actually steady state is 100% achievable when the capacitor current decrease under 1.602176487exp(−19) C/s or so. That's less than 1 electron/second and u can't feed the capacitor less than 1 electron so it's steady state.

Steady state is achieved when there is no change in potential across the plates.  Nobody said anything about 1 second being the criterion, or 5 time constants...both are arbitrary, and I think you should start your prior single electron theory with "once upon a time".  

If you're going to start talking about theoretical 10E-19, single electron stuff, for steady state, the sun will supernova before you stop loading a one electron charge on the cap every 1000 years or so.  You indeed can load an electron every two seconds, or four, or eight, etc

theoretically yours,

-Dr solutions, BS, PhD ("piled higher and deeper")

Posted on: March 03, 2011, 02:25:29 02:25 - Automerged

@tedz n hate....
thanx to u all buddy......
your infos really helped.......
but thinking of 1 thing...........
 if somehow we get an ideal 0 resistance generator
 then will there be no leading or lagging???

A capacitor or inductor are reactances where, by the very definition of capacitor or inductor, there is a phase difference (for the mathematically inclined, an i and j component).  At DC, the reactance is zero, or infinity, again depending on the type of reactance, so phase is meaningless since you are sucking every joule out of the universe and beyond.  

Suggest you get a copy of LT Spice and run these for yourself to get an understanding.  What you are describing is a RESISTOR.  There is no magic in power factor correction....you could build yourself a 3GW nuke plant which could have a source resistance of a few micro-ohms because you have infinite amounts of oil money and are using superconducting alternator coils, have no load on it other than a 2.2uH inductor, and you'll still see the phase difference between current and voltage.

Hmmmm....maybe we've stumbled onto why Iran wants a reactor so badly?

[gan_canny]

It all about electrons . If they are moving ( current) they generate magnetic fields in a plane at right angles to their direction. This relationship is complimentary a changing magnetic field will generate current ( make electrons move). Electrons also generate an electric field. Capacitors take advantage of the electric field  Inductors the magnetic field.
The rate of change of the charge is dependent on the actual charge  (a differential equation)
An electron is a probability wave.
A probability can never be negative it is always between 0 and 100%. All electrons with the same position and spin are identical.
That means they could be interchanged and no one would ever know. Next probabilities when combined are multiplied. Take a coin toss with 50/50 odds two heads in a row is 1/2 x 1/2 or 1/4 ( 25% probability). If we attempt to write a probability equation for the whole universe and include two electrons that are in the same place with the same spin then the equation will have countless combined ( multiplied together) probabilities.For the two electrons( a and b) the probabilities are q(a) and q(b). The equation for the Universe is  q(a)xq(b)x(..every other probability in the universe). Swapping the identical electrons  q(b)xq(a)x( every other probability in the universe) must have the same probability so q(a)xq(b)=q(b)xq(a) now for the twist it turns out electrons are anti commutative q(a)xq(b) always equals -q(b)xq(a) but since electron a is identical to electron b  we can substitute a for b so q(a)x(q(a)=-q(a)xq(a) the only number that will meet this condition is zero so there is always zero probability that two identical electrons are in the same position with the same spin. It's good news for without this behavior there would never be semi conductors. Photons are commutative axb=bxa so there can be ( as in a laser ) many photons in the same position.

[hate]

Nobody said anything about 1 second being the criterion, or 5 time constants...both are arbitrary, and I think you should start your prior single electron theory with "once upon a time".

Well, that's my mistake I should have used 'unit time' instead of 1 sec, but the idea was when the current falls under 1 electron/t(unit time) that means there is no current which also means transient response has died. And in real world u don't have to wait till the last electron when there are lots of outside effects (like EM radiation of all kinds) imposing on the system.
Here are some 'nobody's about '5 Time Constant':
http://eng.iiu.edu.my/~ece_lab/bcl/Exp4%20Sem2%200506.pdf
http://books.google.com.tr/books?id=sxmM8RFL99wC&pg=PA233&lpg=PA233&dq=single+time+constant+transient+response+5+time+constant&source=bl&ots=Er-mVNKT1A&sig=qo1QdCzAP3ItaPuiYIr8dLc-6g0&hl=tr&ei=s2JvTc_dE83HswaswtXwDg&sa=X&oi=book_result&ct=result&resnum=7&ved=0CFAQ6AEwBg#v=onepage&q=single%20time%20constant%20transient%20response%205%20time%20constant&f=false
and there are lots of other introductory texts which u can find out more about '5TC'.

And in case u don't know, 'Sun' will never turn into a 'Supernova' nor into a 'Neutron Star' as it's mass is not enough to become any of these. Instead it will become a 'White Dwarf' and die when the time comes.

[optikon]

hey thanx to all..... really this discussion helped me a lot to make my understandings clearer..

Clearer about what, electrons & time constants or our suns ultimate fate ? :-)

Considering the "quantum" nature of our universe, the real question is how small of a capacitance can actually be generated to accept that one electron.