How to calculate the current that is needed to charge the cable capacitance and inductance while switching DC power supply ON? And the current that is released from the cable inductance and capacitance while switching DC power supply OFF during the transient(charge/discharge) cable stage?

Here is a equivalent circuit diagram:

enter image description here

The parameters R(Ω/m), L(H/m), C(F/m) are known.


The actual equations you want were derived by Lord Kelvin for use on the transatlantic cable system, and the math is known as CABLE THEORY. Interestingly enough, a search on that will likely prove useless, as the most common hits will all be about neurons, for which the same math applies, and finding anything about real cables is difficult.

Interestly enough, the Telegraphers Equations probably do the job (http://en.wikipedia.org/wiki/Telegrapher%27s_equations). That provides all the differential equations you need to do the job. If you need to solve this simultaneously in time and distance, you'll get hyperbolic partial differential equations, and the results will be catenaries involving hyperbolic trig functions (so THAT'S why they're on caculators) if you get to the right answer.

Sorry I can't walk you through the math. It's not simple stuff.

  • \$\begingroup\$ Thank you Scott but is there any easier way to solve that problem? I don't need to know the exact number, just an approximation. \$\endgroup\$
    – Filip
    Feb 20 '15 at 10:16
  • \$\begingroup\$ If you need the steady state solution, derivatives with respect to time go to zero, if that helps \$\endgroup\$ Feb 20 '15 at 11:44
  • \$\begingroup\$ In the steady state, the charging current is 0, and the damping effect from the inductance is also 0, so the sum current is U/R. But I need to know how much current is approximately needed to charge the cable capacitance when turning the supply on and how much current is approximately released from the cable capacitance when turning the supply off and how long does it take. \$\endgroup\$
    – Filip
    Feb 20 '15 at 12:02
  • \$\begingroup\$ Is there a free software tool that can calculate needed parameters ? \$\endgroup\$
    – Filip
    Feb 27 '15 at 9:50

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