I need the differential equation for the following circuit for numerical integration purpose. It is driven by a time dependent current source.

So the question is:

How can I know \$U(t+dt)\$ given \$i(t)\$ and \$U(t)\$?


simulate this circuit – Schematic created using CircuitLab

  • 1
    \$\begingroup\$ Would shorting-out R2 help you find a solution yourself? \$\endgroup\$
    – Andy aka
    Commented Dec 3, 2018 at 11:13
  • \$\begingroup\$ yes, R2 is actually not necessary in the question, as it adds only an offset proportional to the current on the total voltage. I'll simplify the problem \$\endgroup\$ Commented Dec 3, 2018 at 11:16
  • \$\begingroup\$ @Any aka: I gues you mean "opening-out" the resistor. \$\endgroup\$
    – Curd
    Commented Dec 3, 2018 at 13:29

2 Answers 2


enter image description here

Picture taken from this site.


I found it, I actually consider that the current is only charging the cap, and that in parallel the cap is being discharged by the resistor.

\$dv = \frac{1}{C}i(t)dt-\frac{1}{C}\frac{U(t)}{R}dt\$

\$dv =\frac{1}{C}(i(t)-\frac{U(t)}{R})dt\$

and now I can integrate it

\$ U(t+dt)=U(t) + dv\$


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