If I have two cables, with different size, but in total the same resistance, what will be the speed of the current transfer( how much time will it take the voltage to appear at the end of the cable).

for example: Imagine I have two cables, one in the legnth of 1 kilometer, and one in the length of 1 cm. They are made from different materials so in total the resistance of both of the cables is the same. I plug the cables into a circuit, with a capacitor in series, and check the appearance of voltage in the capacitor. If I get just solve the circuit I get the following http://en.wikipedia.org/wiki/RC_circuit#Series_circuit

Is this really to solution for both of the cables.. not matter what is the length of the cables?



Your model describes a short, highly resistive cable where the resistance dominates the cable inductance and capacitance. Such a cable will have such high attenuation that you would never observe signal propagation over very long distances, so the signal speed never becomes an issue.

A long, low-loss cable is well modeled as a series of short segments. The model for each segment of cable is a passive network that accounts for the resistance, inductance, and capacitance within the segment. For a given input signal, one has to solve the entire network of segments in order to find the output vs. time.

Fortunately this was all worked out >100 years ago: http://en.wikipedia.org/wiki/Transmission_line. Basically, one keeps dividing the (fixed-length) cable into ever shorter segments. In the limit of infinitely many, infinitely short, segments, one obtains the telegrapher's equations (see the Wiki article).

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  • \$\begingroup\$ Hi, I was talking about DC and not AC... \$\endgroup\$ – Oren May 25 '15 at 9:35
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    \$\begingroup\$ Since you asked about the time for the voltage to appear, you're talking about pulse transmission, which is calculated using AC techniques. \$\endgroup\$ – Brian Drummond May 25 '15 at 9:51

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