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1-My first question is: when signal with low frequency such as 100khz the wavelength of that is 5 kikometer that means between high and low voltage must be 5 kilometer .so when signal propagate by electron in short circuite (size of circuit is very small than wavelenght)how does electron flow in circuit and 5 kilometer space between the hight and low voltage produce in short circuit???is it true the wavelength of the signal that means:distance of electron travel to reach the first point? If it is true so the signal with 5 kilometer wave lenght produce complete when electron travel 5 kilometer and thus structure repeat.

2-when the size of circuit very small than if wavelength ghen for analysis the circuit we use Kirchhoff's circuit laws Whay the voltage and current in this circuit not change?but in high frequency change I guess in low frequency that wavelength very big than size of circuit the electron have Enough time to reach end of wire and Enough to produce a cycle of signal Because the electron move is very fast and wavelength is very long that the cgarge of electron Enough time to travel on circuit and produce a cycle of wave before next cycle produced. I guess this 2 reason for not change current in length of wire and voltage in first and end of wire is same.is it true?

I know transmission line theory how work. but I dont undrstand whay voltage and current is same in all of the wire lenght,when frequency low and wavelength is very long of size of circuite? in transmission line and maxwell theory happen stand wave because the wave length in antenna and transmission line is proportional lenght of conductor and electron charge not enough time to reach end of conductor befor a cycle if sine wave ended so the electron charge reflected back and stand wave happen this reason of whay antenna work like resonator and radiate with high amplitude. In transmission line and antenna the voltage and charges electron in 1cm and 3cm of wire length is difference because the frequency is very high and wavelength proportional to size of length wire and when electron charge flow in wire because of wavelength the cgarge if electron difrrent in length of wire and no time to reach end of wire and this reason the voltage in length of wire is difference unlike lumbd circuit that voltage same in all length of wire. I dont undrestand this phenomenon how to happen in low frequency and very long wavelength which makes voltage not changed in lenght of wire? is it true the sentence Thanks bro.

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closed as unclear what you're asking by pjc50, PeterJ, Sparky256, ThreePhaseEel, Chupacabras Dec 29 '17 at 9:35

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • \$\begingroup\$ "that means between high and low voltage must be 5 kilometer" I'm not sure if I'm misreading your sentence but I don't think that's how it works. \$\endgroup\$ – tangrs Jun 22 '15 at 1:35
  • \$\begingroup\$ Between the poor spelling and grammar and in-line questions I am a bit confused. I gather your main subject is about standing waves in a conductor. Please clean up your questions so we can make sense of it. I do believe this question has already been answered. \$\endgroup\$ – Sparky256 Dec 28 '17 at 3:58
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Electrons in a circuit move very slowly (much, much more slowly than the speed of light \$c\$). The change in voltage along the line you refer to is due to electromagnetic waves propagation, i.e. varying EM fields that travel along (and around) the line. EM fields travel at a speed that depends on line geometry and on the materials with which is built or that are around it. The traveling EM fields' speed is the one comparable to \$c\$. To compute it exactly you need transmission-lines theory or Maxwell's equations.

Kirchhoff's laws are only an approximation of Maxwell's equations useful for lumped element circuits. They are valid under some assumptions, the most important of which is that the dimension of the circuit \$d\$ must be much less than the minimum wavelength of the EM fields present in the circuit. This is often stated as a requirement on the maximum frequency component of the signals in the circuit:

\[ d << \lambda_{min} \approx \lambda_{0(min)} = \dfrac{c}{f_{max}} \]

Here for simplicity I used the formula that relates the vacuum wavelength \$\lambda_{0}\$ of a plane wave with its frequency. To be strictly correct you should compute the relationship between \$\lambda_{min}\$ and \$f_{max}\$ for the fields in the specific circuit (which is usually an intractable problem, except for very regular geometries such as transmission lines and waveguides). That's usually not a problem because \$\lambda_{0(min)}\$ is usually not very far from the exact theoretical value \$\lambda_{min}\$ and if \$d\$ is sufficiently small everything is OK anyway.

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