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I am a bit confused on the speed of voltage propagation in the transmission line and I hope someone can enlighten me. I understand the speed of step up voltage propagation is in the same order as the speed of light and it is much faster than current. But if we can model the transmission line with a distributed element model as the image below, how can the modelled capacitors got charged so fast at a rate proportional to the speed of voltage propagation if an electron travel much slower?

voltage propagation

Source: All About Circuits - Lessons in Electric Circuits, AC, Transmission Lines, Characteristic Impedance

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The drift velocity of electrons in an electric circuit is indeed slow. However, that doesn't mean that current doesn't "propagate" at very high speeds, often a significant fractions of the speed of light.

To give an analogy, consider a alpine cable car. When the cable pulley is engaged at the top of the mountain, within a very short period the cable all along the way, including the bottom is moving. If the cable system is 1 km and it takes 5 seconds to set the entire cable completely in motion, the "motion" propagates at 720 km/hr. But the cable, and the cars on the cable might be moving at only 2 km/hr.

By analogy, the drift velocity of electrons might be compared to the speed of the cable cars. But the delay between when voltage is applied at one end of a transmission line, and current begins to flow some distance away might be compared to how quickly the cable at the bottom of the mountain begins to move after the pulley at the top is engaged.

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  • \$\begingroup\$ Thanks for answering my question. I did read about some other analogies similar to yours but I don't understand how they can agree with the distributed element model typically used to explain transmission line such as the one in the image. According to the model, propagation requires capacitor to be charged up one after another along the transmission line. If this is the case, that means electrons need to travelling from the + side to the - side in order to charge a capacitor but if electron is indeed traveling very slowly then how can voltage propagate that fast in the transmission line? \$\endgroup\$
    – eyew18
    Commented Sep 12, 2023 at 16:53
  • \$\begingroup\$ @eyew18 Electrons do not travel from one side of a capacitor to the other. \$\endgroup\$
    – Hearth
    Commented Sep 13, 2023 at 3:56
  • \$\begingroup\$ What I meant was electrons move from one plate of the capacitor to the other plate through the voltage source or battery. But it's not important here as long as you agree electrons need to flow from/to voltage source from/to capacitor to charge. \$\endgroup\$
    – eyew18
    Commented Sep 13, 2023 at 7:11

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