studiot

Again short and to the point Mordred. +1

I'm still waiting for an explanation of what forces are involved in boiling a kettle (my post#3) A further question to consider. Why is there no matter or mass whatsoever included in the electrostatic force equation. This equation will function equally well in a universe without any matter since charge itself has no mass.

The effective mass of holes in conductors is generally positive. It is electron behaviour that can require negative effective mass to explain classically.

Especially for Catholics.

Forgive me but was that meant to be a reply to my question. If so I really don't understand so please explain in greater detail.

Not only did I spot it, I liked the way you avoided juxtaposition of self contradictory terms. However this one baffles me Ionise a vacuum? My latest guess is that you want to construct a source of ionized air for test purposes in your goal of recovering energy from already ionised air. I don't know where you are or what your resources are but these guys are really friendly and swop useful kit a lot. http://www.vintage-radio.net/forum/index.php

What happens when you boil a kettle? What force generates the steam as opposed to adding the latent heat causing it?

So here is the first session of a couple or three session crash course in calculusy things. Many authorities advocate teaching integration first and that is probability appropriate here. So what is integration? Well integration is a way of adding things up – it is a sum. Indeed the [math]\int [/math] symbol is the Gothic letter, for the Greek letter[math]\sum [/math] , we use for summation. But it is much more than just summation; it involves adding up lots of products that are the result of multiplying two quantities together. This is very very useful to us in the real world because we often want to do just this. Just to list a few instances. Area = height x Length Distance = velocity x time Heat supplied = specific heat x temperature change Potential Energy = Height x acceleration due to gravity Electrical power = current x voltage Metered electrical energy used = power x time And many many more besides. Integration is often introduced as ‘the area under a graph’ and indeed Area is the first on my list. But integration can provide a great deal more since calculating the left hand side of each equation involves some sort of integration of the right hand side. Important points about my list The enormous number and variety of quantities encompassed. Some of the quantities are variables, some are constants. Some of the multiplied quantities have the same units, some have very different ones. A consequence of (1) is that when we come to write things out as mathematical expressions we have a symbols problem. Because we have only a few symbols to work with, mostly Roman and Greek letters, some must do double (or more) duty. Care must then be taken to avoid confusion different quantities represented by the same symbol as happened in your opening post with watts (power) and work (energy). Further it is sometime difficult to choose which common quantity to represent by the first letter for example voltage or velocity, distance or diameter, etc. Now let us look at the format of an integral [math]\int\limits_{x = a}^{x = b} {\left( {{\rm{expression}}} \right)} dx[/math] We see the product of two quantities, (expression) and dx to the right of the integral sign and two statements about different values of the variable x associated with the integral sign itself. This brings us to point (2) above some quantities are variables and some are constants. We choose one of the variables as the base variable for the integral. This is called the running variable or the independent variable or in some cases a parameter. The dx part is always in terms of the running variable - x in this instance. The point is that the integral covers a range of values of this variable, not just one as is the case with a constant. So we can’t use a constant as the base. The range of values taken on by the running variable is starting at the value at the bottom of the integral (x = a ) and extending to the value at the top (x = b) and covering all values in between. In order of difficulty the (expression) can be A constant An expression in the running variable – x in this instance An expression in another variable. So what to do with this integral? If we take the black box from my post#10 and define the process inside the box as “Look up the integral for (expression) in a table of standard integrals and then write the result within square brackets we have” [math]\int\limits_{x = a}^{x = b} {\left( {{\rm{expression}}} \right)} dx = \left[ {{\rm{Integral}}\;{\rm{from}}\;{\rm{tables}}} \right] = \left[ {{\rm{new}}\;{\rm{expression}}} \right]_{x = a}^{x = b}[/math] Then we write the beginning and end values of the running variable at the end of the square brackets. I have used the full version x=a, x=b to make it clearer, but the x= part is often dropped. However keeping the x= is not onerous and helps when we come to part 3 on the list and change of variables, which you had trouble with. We evaluate this by putting the values of x at b and a into the new expression and subtracting thus. [value of new expression at x=b] - [value of new expression at x=a] (Note which is subtracted from which) To see how this works let us look at the simplest possible examples. If (expression) = 1 (that’s right one) And a = 0 and b = 1 we have [math]\int\limits_{x = 0}^{x = 1} 1 dx = \left[ {{\rm{Integral}}\;{\rm{from}}\;{\rm{tables}}} \right] = \left[ {{\rm{new}}\;{\rm{expression}}} \right]_{x = 0}^{x = 1}[/math] If we look up the integral of 1dx in tables we find it is x so putting this in we have [math]\int\limits_{x = 0}^{x = 1} 1 dx = \left[ {{\rm{Integral}}\;{\rm{from}}\;{\rm{tables}}} \right] = \left[ {\rm{x}} \right]_{x = 0}^{x = 1} = \left( {\left[ {x = 1} \right] - \left[ {x = 0} \right]} \right) = \left[ 1 \right] - \left[ 0 \right] = 1[/math] We now have something we can start applying to your original post, so I will stop there and post this and await feedback.

Very quickly (there could be more, I have a good deal spread about.) is this the sort of thing you are looking for? https://books.google.co.uk/books?id=DSHSqWQXm3oC&pg=PA936&lpg=PA936&dq=pulse+terminology&source=bl&ots=o0QQEMJH9R&sig=QPagCDwrh4-bV2zeC5SGczqngf0&hl=en&sa=X&ved=0ahUKEwjunfbq7svTAhWpLsAKHfLCChM4ChDoAQgUMAA#v=onepage&q=pulse%20terminology&f=false

Don't worry it will all become clear as I work through it. But it will take a little time to write out all the maths. So I have posted this since I see you are online right now.

Hi Ed, I don't disagree with what you are saying. But it is not the vertical axis that is the problem it is the horizontal one. Any self respecting pulse generator has a DC offset controll that will move the generated pulse train up and down on the vertical axis. Any receiving circuitry can alter this to suit, with simple blocking capacitors / DC restorers at will. None of this will affect the basic nature of the pulse train. However the generator will have not one but two oscillators to generate the pulses if it has variable mark/space ratio. This is because there are inherently two independent frequencies in play in pulse generation. Each frequency is needed to define the two halves or aprts of the pulse train. If the pulses are of very short duration ( very small mark/space ratio) then that part of the pulse will need much higher frequency circuitry to handle it. You didn't answer my question in post#21? Did you look up magnetohydrodynamics, the techniques there seem ideaaly suited for your needs. You should also look up the work of Nobel prize winner Alven https://en.wikipedia.org/wiki/Alfv%C3%A9n_wave

Hi mondie, it is kinda difficult for me to know how to help wihtout at least some reaction to my last post. My next step wouold be to work through your posted example maths, line by line. But I don't know if you are interested in the maths or the electrical engineering?

Hi Ed, yes there are several viewpoints and I know that many (including Wiki) use the term pulse frequency without much thought. The problem is Consider a pulse, 10 nanoseconds long, repeated every 10 microseconds. What are you using to define the frequency the 10 nanoseconds or the 10 microseconds? Do you think a circuit with a bandwidth of 100khz would pass this pulse train? The term frequency can be used with some meaning for a square wave and you could expect a square wave with an 'on' time of 5 microseconds and an off time of 5 microseconds to pass such a circuit with some rounding but a still appearing as a recognisable square wave. Very short pulses need additional information to describe them properly, which is why radar engineers invented PRF and all the other terms. Your interposing cloud of electrons would appear to me to constitute a plane rather than a pulse?

The math huh http://mathworld.wolfram.com/DeltaFunction.html There are some pretty pictures of a sine expansion, amongst others. But see also my response to Strange below. I particularly liked your last sentence, emboldened, especially the bit about pulsed DC, which is what I was talking about and Handy would be generating. What exactly is the non zero portion of a perfect pulse if not DC? It is a stright line parallel to the horizontal axis. Because of this when designing say pulse transformers or transmission lines etc it is common to break the puls into three sections. Section 1 The rising front is analysed by high frequency equations since it has many high frequency components, Section2 The flat top is analysed by DC or low frequency analysis since it ideally has zero freqency components Section 3 The trailing edge is analysed by HF analysis as the leading edge. An additional pulse characteristic called droop is introduced in real world analysis of section 2. This sort of situation appears in radar systems, and in analog power supplies where enormous current pulses occur for very short durations during the reservoir charging/discharge cycle. See here particularly the quote underlined. http://www.thefouriertransform.com/pairs/impulse.php Frequency = 1/wavelength yes? So what is the frequency of a zero length pulse? So I am saying that both terms are inappropriate for some repetitive and non repetitive 'generalised' functions. We see these in solitons, heaviside impulse functions and dirac functions amongst others.

Good evening Ed. Can you explain how something which does not cross zero for its duration, but remains at a constant level can have a frequency? I note the linked article also refers to PRR. The actual characteristics I gave are the bare minimum. In practice more may be needed for circuit design purposes.

Hello and welcome. Thinking up new ideas is to be encouraged, especially when you try to explain observed effects We call our propositions 'hypotheses' not theories which is what a hypothesis becomes after substantial verification. However it is always as well to make sure that you get your facts straight so deflection of light by magnetism? see here http://www.bbc.co.uk/education/guides/z996fg8/revision/4

Apologies mondie, I only looked at the worry over square brackets so I didn't notice you had displayed some. If your entire post #1 is confusing you, it is certainly comfusing me to unravel. I'm not sure why you are reading an electrical engineering book. Are you now studying electrical engineering? There was a long discussion on an electrical engineering forum where many engineers observed that although they learned calculus in college, they never used it in their working life. But they had to know calculus to pass their exams to become electrical engineers. Further complications for here are added because those studying electrical engineering at college (you will not meet those equations in school) are expected to have some basic physics so they understand that power is the rate of doing work and that energy is work times time. Further you have mentioned Ohms law for an inductor incorrectly. Your equation is Faraday's law of induction except that you have missed out the all important minus sign which shows that the induced voltage opposes the change in current. You also stated that you haven't taken a calculus course so not suprisingly you are struggling with the equations incolving calculus. I am now going to offer you an alternative life view called black box theory. Black box theory originated (I think) with electrical engineers, but it has spread to many disciplines. It is heavily used in electrical engineering and has the advantage that it can use both digital and analog techniques. Essentially you have a black box with an input and an output. The output is a well defined function of the input. But you don't worry how it works inside the box. The black box may be a physical device such as a breadmaker where the inputs are ingredients and the output is a loaf of bread; or it may be theoretical where the input is a number and the output is the square of that number. In the first example I have shown the basic box. I have added one extra line called control. This control allows me to vary the output that is produced from a given input. The second example is a nice double your money machine or scheme. The third example is the Las Vegas version. The fourth example takes a mathematical function and outputs the derivative of that function. The fifth example does the same for an integral, but also uses the control input to apply the boundary condions or the limits of integration. The final example is known as a two port network and is a fundamental building block in electrical circuit theory. So help us to help you by saying where you are coming from and where you want to go to. Are you interested in the Physics, the Electrical Engineering or the Mathematics, because, without black box methods, you need to get all of these right to succeed.

It's true that the thermite process now encompasses a wide variety of fuels. https://en.wikipedia.org/wiki/Thermite

You don't need a grenade for some fun spectacular burning and fuels. You can set fire to an iron rod if you heat it hard enough and then it will burn fiercely enough to cut through concrete and steel.

I am suprised at Schaum. They are usually pretty clear as they are designed for exam cramming. Difficult to comment on one I don't have. Do your square brackets look something like this? [math]\int\limits_0^1 {xdx} = \left[ {\frac{{{x^2}}}{2}} \right]_0^1 = \left[ {\frac{{{1^2}}}{2} - \frac{{{0^2}}}{2}} \right] = \frac{1}{2}[/math]

This discussion over tungsten filaments is a little esoteric, surely? The higher the filament temperature the whiter the light produced. Tungsten is used for filaments as it has the highest melting point of any metal a bit over 3400o K. However it has a positive coefficient of resistivity with temperature so as the filament heats up the resistance rises. This is fortutious as this means the current drops to a self limiting value. The filament resistance increases to nearly 20 times its cold (room temperature) value by the time it is near melting.

No problems we are all friends here and friends help when someone has had too much tequila.

Surely not because that would imply that the resistance of the conductor would disappear if you took the voltage away. The resistance of a material has nothing to do with the voltage applied to it in general. (Yes I know there are such things as VDRs)

No there can't be an infinite number of them whilst the particle is in the atom. There is a defined, finite, set of energy levels before any particular electron leaves the electron and the atom becomes an ion. At this point the energy spectrum of the electron becomes continuous, and therefore comprised of an infinitude of levels, although there is some debate as to whether it is actually continuous or made of incredibly finely divided levels.

I note you are seeking a basic explanation so There are two ways to approach this. The electrical engineer's approach which is offered at elementary level, even in Physics. Bender has already begun this. This is empirical (based on observation and experience) and simply accepts there is a property we call resistance that connects more basic electrical properties by Ohms Law. The physicists approach. However physicists do not (usually) work in terms of resistance. They study conductance, which is the reciprocal of resistance. This allows them to study why wires and other things conduct at all. So if we take Ohms Law V = IR and the observation that the power dissipated equals the product of the voltage and the current, P=IV we can generate two new equations. [math]P = IV = I(IR) = {I^2}R[/math] [math]P = IV = \left( {\frac{V}{R}} \right)V = \frac{{{V^2}}}{R}[/math] Now the power dissipated ends up as heat, so this tells us where the heat in your question comes from. The first equation tells us that the power dissipated is directly proportional to the square of the current and to the resistance. So if we maintain the current at a constant level and increase the resistance, more heat will be generated. However, and this is very important, Ohms Law tells us that you cannot specify all three of resistance, current and voltage. Once you have specified two of them the third is fixed (by Ohms law). So if we specify the current, and change the resistance, the voltage must vary to suit (goes up). But, as Bender pointed out, most electrical supplies (batteries, the mains and so on) have a fixed voltage. So if the voltage is fixed and we increase the resistance the second equation shows an inverse proportionality between power and resistance. So the power goes down if fix the votlage and increase the resistance, but the current varies goes down to suit. OK so this is all empirical. But why does things conduct at all and what is resistance? Well this question is not studied until university/college level physics and even today is not fully understood. There are several theories including the free electron theory and the band theory. Here is a non mathematical roundup. It is an observed fact that different materials conduct electricity to differing degrees. We distinguish three main categories Conductors Semiconductors Non Conductors In the free electron theory differning materials are able to release or free some (a very small proportion) of their electrons. These electrons are free to move about within the solid and become responsible for the ability of the material to conduct. Of course they leave behind much more massive atoms or ions, firmly locked in the lattice of the material. It is a good job these are not also free to move about or the material would fall apart! These free electrons 'drift' around in aimless or random fashion, moved on by thermal agitation. So there is no net movement in any direction. If we then impress a voltage difference the electrons are pushed in a preferred direction by this voltage. The greater the voltage, the more electrons are moved. A net movement of charge (electrons) constitutes a current so we have Yes you guessed it Ohms Law! The net current is proportional to the voltage. Now in a perfect crystal these free electrons are completely free to move. This is due to the perfectly regular nature of a perfect crystal exactly matching the quantum requirements for movement. Perfect crystals have zero resistance. But no crystal is perfect, certainly not the crystals making up a wire. There are several different imperfections, but all imperfections offer some resistance to free electron movement in their immediate environment. Imperfections include Impurities The fact that the wire is made of lots of small crystals joined together at random orientations so the moving electrons keep coming up against crystal boundaries. Thermal vibration distorting the perfect regularity of the lattice as the fixed ions/atoms vibrate about their mean positions. Does this help?