I'm expecting a midterm question about the circuit below that involves the equation t=RC and using a Laplace transform. We won't actually be using differential equations. Memorizing a certain equation is all we need, but we're not told what it is. I've found a lot of equations when looking up Laplace transforms. Which equations would be helpful for analyzing this circuit, and where in the circuit could they be applied?

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  • \$\begingroup\$ So what good does it do you if we just tell you the answer? \$\endgroup\$
    – W5VO
    Mar 23, 2011 at 9:21
  • \$\begingroup\$ @W5VO Moot question because we won't do it. :P \$\endgroup\$
    – jpc
    Mar 23, 2011 at 12:23
  • \$\begingroup\$ Find the laplace form and matrix of the electrical circuit given above, provided that the starting condition is 0 \$\endgroup\$
    – Yusuf
    Jan 18, 2021 at 23:15

1 Answer 1


Using the Laplace transform in circuit analysis works just like normal complex analysis. You just plug \$s\$ instead of \$j\omega\$ everywhere.

Laplace circuit analysis rules from Wikipedia

The interesting part comes after you calculate one thing or another since you can use Laplace transfer function to draw a Bode (frequency and phase response) plot or to calculate the circuit's response to any stimulus.

  • \$\begingroup\$ Why are those voltage/current sources there? That makes no sense to me. \$\endgroup\$
    – Jason S
    Jun 11, 2011 at 0:10
  • \$\begingroup\$ @Jason the voltage/current sources are in the s-Domain models because a capacitor/inductor can act like a time dependent voltage or current source. Also, each have a frequency dependent resistance (impedance), which is why the resistor is in the model. \$\endgroup\$
    – gallamine
    Jun 13, 2011 at 16:04
  • 1
    \$\begingroup\$ @Jason They represent the current or voltage at t = 0 and are needed to account for the energy stored inside the reactive elements. \$\endgroup\$
    – jpc
    Jun 25, 2011 at 1:05

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