Inductors Charging

by flexifirm
Tags: charging, inductors
 P: 657 The point is,I don't think the wL actually plays the same role as the resistance,and therefore is not the analogue of resistance because: 1. In Ohm's law,the voltage directly determines the current ,whereas in an inductor,the voltage determines the rate of change of current,so we can't just say the current due to the voltage is reduced by a factor of wL,like we would in case of a resistance. 2. wL is just a result of integration....does it have to have a physical existance? 3. The inductor doesn't exactly oppose the current (on the long run).....since,as The Electrician said,for a pure inductor with a dc supply attached,the current would increase forever. Also,some queries in regard to impedance... 1.the wL is supposed to determine the amount of power loss there is in the circuit due to the 'storage of energy' in the inductor......but in an ac circuit,the energy is continuously taken and given back by the inductor...so really,there isn't any loss at all. 2.The reactive power due to the inductor is supposed to be VIsin(phi),where Vand I are the RMS values....why do we take RMS values (on the long run,power loss is zero,so even if we do get a certain value of RMS,it wouldn't make sense.) 3. I don't understand why we assign the 'sin(phi) ' part of the expression...as if the reactive power is a component of total power (it might make sense for the phasor representation,but it doesn't make sense physically,it seems).
P: 190
 Quote by Urmi Roy 3. I don't understand why we assign the 'sin(phi) ' part of the expression...as if the reactive power is a component of total power (it might make sense for the phasor representation,but it doesn't make sense physically,it seems).
Actually, here total power might mean 'Apparent power' and not necessarily only 'wattful' or 'active' power. Since reactive power is a component of Apparent power (total power) and reactive amps are ideally 90 deg out of phase hence representation by sin(phi).
P: 657
 Quote by b.shahvir Actually, here total power might mean 'Apparent power' and not necessarily only 'wattful' or 'active' power.
I understand that it's the apparant power that is mentioned in the formula.....but again,the word 'component' may be meaningful in case of vectors and phasors,which have directions....but in reality..or in the actual physical world,the current,power etc. can't have directions!

Also,could you have a look at the rest of my questions?
P: 190
 Quote by Urmi Roy I understand that it's the apparant power that is mentioned in the formula.....but again,the word 'component' may be meaningful in case of vectors and phasors,which have directions....but in reality..or in the actual physical world,the current,power etc. can't have directions! Also,could you have a look at the rest of my questions?

Current has magnitude as well as direction.
Could you pls. ennumerate in brief the points you are after.
 P: 657 Let me first start off with my basic problem: In an inductor,there is no loss of power on the long run....whatever it takes away,it gives back. Now,still,we define something called the 'reactive power',which is VIsin(phi)......but I just can't make sense of why we consider the RMS voltage and current,when there is,infact no loss of energy. Also,it is said that the RMS voltage and current accross the inductor and resistor in a RL ac circuit are equal.....how? The voltage and current in an inductor and resistor cannot be equal simultaneously,can they?
P: 670
 Quote by Urmi Roy Let me first start off with my basic problem: In an inductor,there is no loss of power on the long run....whatever it takes away,it gives back. Now,still,we define something called the 'reactive power',which is VIsin(phi)......but I just can't make sense of why we consider the RMS voltage and current,when there is,infact no loss of energy.
First of all, let's talk only about single frequency sinusoidal waves.

Since we human beings usually want to do something with voltages and currents, there will ultimately be some resistance or load somewhere that will dissipate power. If we use RMS quantities then our computations are simpler when the usage of power comes into play.

Otherwise, you could use any kind of measure: peak-to-peak, peak, average.

The reactance of an inductor, wL, is just the ratio of the voltage to the current at a frequency, and does not depend on the kind of measure.

 Quote by Urmi Roy Also,it is said that the RMS voltage and current accross the inductor and resistor in a RL ac circuit are equal.....how? The voltage and current in an inductor and resistor cannot be equal simultaneously,can they?
P: 657
The fact that the rms of the voltage and current through an inductor are considered must imply that we are talking about one particular half cycle or something....since after the second half,when the entire energy is delivered back,the measure does not have any significance....considering it over a half cycle will allow us,perhaps to calculate the thickness of the wire needed to carry that current,during that time.

Also,'The Electrician',could you please throw some light on the analogy between resistance and reactance that I referred to in post 55?

 Quote by The Electrician The reactance of an inductor, wL, is just the ratio of the voltage to the current at a frequency, and does not depend on the kind of measure.
Does the bolded part have any special implication?
P: 670
 Quote by Urmi Roy The fact that the rms of the voltage and current through an inductor are considered must imply that we are talking about one particular half cycle or something....since after the second half,when the entire energy is delivered back,the measure does not have any significance
This is not so. The RMS value of a voltage of current is a measure used when we're talking about a steady state situation. It doesn't apply to transient currents such as were discussed earlier in this thread. But if you say that the voltage at the wall socket is 120 VAC (in the U.S.), that means the RMS value is 120 volts, whether for just one full cycle, or many cycles. When you calculate the RMS value of a waveform, you must make the calculation over at least one full cycle. See:

http://www.ee.unb.ca/tervo/ee2791/vrms.htm

It has nothing to do with the direction of energy flow. Suppose you look at the voltage waveform applied to some component, a resistor, a capacitor or an inductor, but you don't look at the current. Assume you don't even know what kind of component you're using. The direction of energy flow depends on both the voltage and current, but you don't know the current (by my hypothesis), so you don't know anything about energy flows.

You can still calculate (or measure) the RMS value of the voltage even though you don't know what kind of component the voltage is applied to, or what kind of energy flows may be taking place.

 Quote by Urmi Roy Also,'The Electrician',could you please throw some light on the analogy between resistance and reactance that I referred to in post 55?
Reactance plays the same role as resistance in the following sense: If you apply a single frequency sine wave of voltage to an inductor, a very specific current will flow. The current will not be infinite as it would if the applied voltage were DC. The inductor will limit the current to a finite value. The ratio of the voltage to the current will be E/I = wL, the reactance of the inductor at the operating frequency.

When you apply a voltage to a resistor, DC or AC, the resistor limits the current, and the ratio of the voltage to the current is E/I = R. R is completely analogous to resistance; it expresses the opposition to the flow of current.

It doesn't matter if there is temporary energy storage or not. All that matters to make the analogy between resistance and reactance in AC circuits is that, when you apply a voltage to a component, the magnitude of the current is determined by the component in some manner, whether by dissipation of energy, or by back and forth exchange of energy.

 Quote by Urmi Roy Does the bolded part have any special implication?
The implication is just what I said in the previous sentence. "Kind of measure" means the method of measurement of a current or voltage. The three I mentioned were peak-to-peak, peak and average. For the measurement of AC quantities, strictly speaking the average of a sine wave is zero. When, for example, a meter is referred to as average responding (rather than RMS responding), it means to rectify the AC and then take the average.

If you apply a 120 volt peak-to-peak sine wave to an inductor, and measure the current as a peak-to-peak quantity, the ratio of the peak-to-peak voltage to the peak-to-peak current will be wL, as it will be if you measure as a peak voltage, or an average rectified voltage.

The ratio of voltage to current (for a single frequency sine wave) will always be wL, if you use the same measurement units for both voltage and current.

I explained the reason for preferring RMS in post #60.
 P: 657 From your explanation about the reactance and resistance,what particularly struck me was :"The current will not be infinite as it would if the applied voltage were DC. The inductor will limit the current to a finite value." So though reactance is not exactly similar to resistance,for our mathematical convenience,we define (omega)L as reactance and say it's similar to resistance...right? Also,as I said earlier,there is a sin(phi) when we define the reactive power in terms of VIZ,where Z =impedance,Iand V are RMS values......firstly,I presume this sin(phi) is a fixed value,and not changing (like what we usually do in analysis of RL/Rc/RLC circuits,where the arrow rotates)...... secondly,the fact that the quantity impedance being defined as the (square root of the (reactance squared + resistance squared))...is it just a ,mathematical convenience? Afterall,the currents,reactances,resistances don't really have directions and obey pythagora's theorem,right?
P: 670
 Quote by Urmi Roy From your explanation about the reactance and resistance,what particularly struck me was :"The current will not be infinite as it would if the applied voltage were DC. The inductor will limit the current to a finite value." So though reactance is not exactly similar to resistance,for our mathematical convenience,we define (omega)L as reactance and say it's similar to resistance...right?
I think it may be of help to you to read this:

and any other references you can find dealing with "the impedance concept". The point of the impedance concept is that in every situation where there are physical quantities analogous to "pressure" and "flow", there is inevitably a relationship between the two which is an "impedance".

Resistance is not "exactly" similar to reactance in every respect, but in the single respect that it determines the relationship between voltage and current in a two terminal device, the similarity is exact.

 Quote by Urmi Roy Also,as I said earlier,there is a sin(phi) when we define the reactive power in terms of VIZ,where Z =impedance,Iand V are RMS values......firstly,I presume this sin(phi) is a fixed value,and not changing (like what we usually do in analysis of RL/Rc/RLC circuits,where the arrow rotates)...... secondly,the fact that the quantity impedance being defined as the (square root of the (reactance squared + resistance squared))...is it just a ,mathematical convenience? Afterall,the currents,reactances,resistances don't really have directions and obey pythagora's theorem,right?
Have you ever seen any explanation of impedance where it was claimed that "...currents,reactances,resistances..." have directions? I think you're overanalyzing.

Complex numbers can be represented as directed line segments (vectors) on the two dimensional plane. The arithmetic of vectors is the same as the arithmetic of complex numbers in the essentials that relate to analysis of electric networks. Often having an analogous representation can assist understanding, but that doesn't mean that the two things are the same. They're just analogous in some aspects, some behaviors.

The earlier reference I gave mentions Steinmetz's discovery that the differential equations of circuit theory could be solved with simple algebra of complex numbers. This doesn't mean that currents in inductors are imaginary.

It's more than just a mathematical convenience; it's a necessity for solving a circuit. The solution of networks is an excellent example of applied mathematics. A mathematical process that behaves the same way as some physical quantities is discovered, which can then can be used to determine the behavior of the physical system. As I said, this is more than a convenience; it's a necessity to analyze and design circuits.
 P: 657 The page isn't opening....apparantly,it's damaged...is there any similar page? Anyway,from your post,the ethos seems to be that the issue of 'impedance' is an essential mathematical tool. Please confirm one vital thing for me... We say that the rms current I is equal through both the resistor and the inductor.... Then, Vrms=Vr+Vl (Vr and Vl are the potential drops accross the resistor and inductor at any instant respectively.) Vrms=Ir+jIX then the magnitude of Vrms= root over((Ir)^2 + (IX)^2) ....1.the fact that I is considered equal for both the components must be due to the fact that over time,the net charge transferred through the inductor and resistor are the same.... 2..and the fact that the voltage accross the inductor and resistor are always at a phase difference of 90deg,so averaged over time,the Vrms arrow must be represented as the hypotenuse of the right angeled triangle. Sorry if this is getting too frustrating....
P: 670
 Quote by Urmi Roy The page isn't opening....apparantly,it's damaged...is there any similar page?

 Quote by Urmi Roy Anyway,from your post,the ethos seems to be that the issue of 'impedance' is an essential mathematical tool. Please confirm one vital thing for me... We say that the rms current I is equal through both the resistor and the inductor.... Then, Vrms=Vr+Vl (Vr and Vl are the potential drops accross the resistor and inductor at any instant respectively.) Vrms=Ir+jIX then the magnitude of Vrms= root over((Ir)^2 + (IX)^2)
You say: "Vrms=Vr+Vl (Vr and Vl are the potential drops accross the resistor and inductor at any instant respectively.)"

I assume that you mean for Vrms to an applied voltage across a series combination of a resistor and an inductor. The way you've described it, Vr and Vl are the instantaneous voltages across each component. If that is so, then Vrms is not equal to Vr+Vl; Vrms is a kind of average, not equal to a sum of instantaneous voltages.

This is not so. When we speak of an RMS voltage or current, we denote a magnitude. Anytime you say Vrms, it's a magnitude. In your very next sentence: "then the magnitude of Vrms= root over((Ir)^2 + (IX)^2)" you show the proper way to find the resultant of the two individual voltage drops; a simple sum is not correct.

 Quote by Urmi Roy ....1.the fact that I is considered equal for both the components must be due to the fact that over time,the net charge transferred through the inductor and resistor are the same....
Well, of course. For two components in series, the current through each is not just "considered" equal (for some mathematical convenience); it is physically identical in each component, which is indeed the same thing as saying "over time,the net charge transferred through the inductor and resistor are the same"

 Quote by Urmi Roy 2..[/B]and the fact that the voltage accross the inductor and resistor are always at a phase difference of 90deg,so averaged over time,the Vrms arrow must be represented as the hypotenuse of the right angeled triangle. Sorry if this is getting too frustrating....
This description of a "phase difference of 90 degrees" is only relevant in the steady state with a single frequency sine wave applied to the series combination. A non-sinusoidal voltage waveform still has a well-defined RMS value. To get the current in the non-sinusoidal case, you have to solve the circuit differential equation for the applied voltage, and the applied RMS voltage is not related to the individual voltages according to a single right triangle analogy.

But, yes, for a single frequency sine wave you can use the right triangle analogy, although I would say "can be represented as the hypotenuse" rather than "must be represented as the hypotenuse". Triangles need not be brought into it at all. A person who knew nothing about the geometry of triangles could still solve for the resultant of the voltage across a series connected resistor and inductor using the square root of the sum of the squares formulation.
P: 657
 Quote by The Electrician You say: "Vrms=Vr+Vl (Vr and Vl are the potential drops accross the resistor and inductor at any instant respectively.)" The way you've described it, Vr and Vl are the instantaneous voltages across each component. If that is so, then Vrms is not equal to Vr+Vl; Vrms is a kind of average, not equal to a sum of instantaneous voltages.
This is exactly what I was getting at...but my book derives it this way!I am aware that the rms voltage cannot be represented as the simple sum....I suppose my book must be wrong somewhere.

 Quote by The Electrician Well, of course. For two components in series, the current through each is not just "considered" equal (for some mathematical convenience); it is physically identical in each component, which is indeed the same thing as saying "over time,the net charge transferred through the inductor and resistor are the same"
The reason I'm stressing on this is because here I is the rms current...and I have a feeling that the instantaneous current in a RL circuit cannot be equal for both the resistor and inductor can it?.....I mean,while the resistor is conducting current according to applied voltage,the inductor is busy trying to oppose the change in current.
P: 670
 Quote by Urmi Roy This is exactly what I was getting at...but my book derives it this way!I am aware that the rms voltage cannot be represented as the simple sum....I suppose my book must be wrong somewhere.
Can you post a picture of the page(s) in your book where they derive this?

 Quote by Urmi Roy The reason I'm stressing on this is because here I is the rms current...and I have a feeling that the instantaneous current in a RL circuit cannot be equal for both the resistor and inductor can it?.....I mean,while the resistor is conducting current according to applied voltage,the inductor is busy trying to oppose the change in current.
You are imprecise in the way you say things. You left out an important qualifier that makes all the difference.

You said: "...the instantaneous current in a RL circuit cannot be equal for both the resistor and inductor can it?"

It absolutely is the case that the instantaneous current in a series RL circuit is identical for both the resistor and inductor.

This is the property that characterizes a series circuit; the current in all the components that are in series is the same.
P: 657
 Quote by The Electrician Can you post a picture of the page(s) in your book where they derive this?
It's difficult to post the picture of the pages,as I don't know anywhere in my campus where they give students acess to scanners....but I can copy it out and promise that I'm copying the exact thing out,if you want.
P: 670
 Quote by Urmi Roy It's difficult to post the picture of the pages,as I don't know anywhere in my campus where they give students acess to scanners....but I can copy it out and promise that I'm copying the exact thing out,if you want.
Can't you take a picture with a cell phone camera, yours or a friend's? Or just with a regular digital camera?
 P: 657 I tried to take a picture on my camera.... Attached Thumbnails
 P: 670 OK, but this doesn't show how they calculated Irms.

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