I was learning to work with RLC circuits with sinusoidal excitations and the book I was dealing with showed me that the responses of these passive elements to sinusoidal excitation were themselves purely sinusoidal and hence phasor digarams were the best way to deal with these elements, but then I tried solving a simple series RLC circuit using laplace/complex frequency analysis and I landed myself a sine term, a cosine term and a real exponential term. I don't know what or why I am getting that real exponential term, I tried to do it over and over and I got the same results. I am pretty sure my calculations are correct but the book mentions nothing about the exponential term. Kindly pitch in...

This is the circuit I was talking about


simulate this circuit – Schematic created using CircuitLab

Here is an image for a KVL and laplace transformationKVL and Laplace

Here is an image for the inverse after separation. I dont think there is a mistakevariable separation and inverse

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    \$\begingroup\$ Why don't you show us the circuit you are trying to analyze and the work that you have done? My internet connection is too slow to read your mind. \$\endgroup\$
    – Joe Hass
    Mar 22, 2014 at 13:04
  • \$\begingroup\$ I uploaded the circuit, will upload my equations in a minute... \$\endgroup\$ Mar 22, 2014 at 13:23
  • \$\begingroup\$ Where is the "L" in your circuit? The circuit you provided doesn't have an inductor, but you said it was a series RLC circuit. \$\endgroup\$
    – Joe Hass
    Mar 22, 2014 at 13:43
  • \$\begingroup\$ No, for this circuit there is no L, just a R and a C and sinusoidal excitation. \$\endgroup\$ Mar 22, 2014 at 13:45
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    \$\begingroup\$ Clearly you have tried to solve this on your own, and your work is incredibly neat for a student. You certainly do not look foolish. But as Dave Tweed said, this isn't a good place for the kind of tutorial you need. I would suggest that you look for circuit analysis books at your school's library. Even pretty old books would cover this material. \$\endgroup\$
    – Joe Hass
    Mar 22, 2014 at 14:01

1 Answer 1


That real exponential term represents the transient response of the system. Generally, when doing steady-state sinusoidal analysis, you can simply ignore the transient response altogether, since the real part of the exponent is usually a negative value times t (time), which goes to zero as t → ∞. If not, it means the system is unstable to begin with.

  • \$\begingroup\$ Okay. Thank you for your answer. Is there any substantial literature on transient responses during sinusoidal excitation, because where I am studying from they simply forgot to tell me anything whatsoever about it and assumed that I'd learn by making a fool out of myself on a public forum.. \$\endgroup\$ Mar 22, 2014 at 13:30
  • \$\begingroup\$ No, it isn't foolish to ask for information. However, it is a very broad subject that will be difficult to handle in the Q&A format used on this site. Any decent college level textbook on circuit analysis should cover it in detail. I learned this stuff back in college myself, and I don't really have any online references that I can point you to. Perhaps someone else can help. \$\endgroup\$
    – Dave Tweed
    Mar 22, 2014 at 13:39
  • \$\begingroup\$ I'm sorry to have sounded crass, I was just a little pissed at the whole scenario. I was going on and on about the exponential term the whole day and I got a genuine answer about around 5-6 hours of head banging. Thank You very much for your help anyways, I really appreciate it. \$\endgroup\$ Mar 22, 2014 at 13:43

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