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I am currently learning control system design. I have a lot of confusion about the initial conditions of the inductor in the circuit. Could someone please correctly solve this by getting the differential equations and then take the Laplace transform.

  • \$\begingroup\$ You must show your attempt at constructing the differential equation. For the initial condition, assume the circuit has been connected for a long time, therefore the initial current is constant. \$\endgroup\$
    – Chu
    Commented Apr 29, 2019 at 6:28

1 Answer 1


Using Faraday's law of induction, we can write:


Where \$\text{I}\left(t\right)\$ is the input current (which is the same trough all the components because it is a series circuit).

Using Laplace transform we can write:


  • \$\begingroup\$ Can you explain to me the significance of the I(0), the initial current for the inductor ? Because in some other examples I've seen they don't include that even though the Laplace of the derivative has it. \$\endgroup\$ Commented Apr 29, 2019 at 7:44
  • \$\begingroup\$ @MaizHalyym Well that is the initial condition in this circuit. So when there is an initial current trough the inductor it has to be placed there. \$\endgroup\$ Commented Apr 29, 2019 at 8:00

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