I'm solving a question in Linear circuit analysis 2 class. the question is to analyze a switching circuit with inductors and capacitors. this is the circuit in the time interval drawn in S-domain using laplace tranform with initial conditions for the inductor and capacitor already considered. if I want to find , what will the current passing in the second branch from the left be?? and what would the node equation look like?

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  • \$\begingroup\$ Are VI(s) and Vc(s) actually measuring the same thing (the potential between the "top" node and the "bottom" node, or does VI(s) have its negative contact between the voltage source and the 20-ohm resistor? \$\endgroup\$ – The Photon May 11 at 14:52
  • \$\begingroup\$ What is the circuit prior to t =0? \$\endgroup\$ – Andy aka May 11 at 15:35
  • \$\begingroup\$ Vl is the voltage of the inductor with the voltage source in series which is the initial condition LI(0-) at t >= 0, the sane goes with the capacitor voltage with the capacitor and the current source ( initial condition CVc(0-)) , so yes, it is between the resistor and the voltage source \$\endgroup\$ – Obada May 11 at 16:11
  • \$\begingroup\$ Andy, I have tried to cut everything short and give Only what is relevant to my question, What information do you need in particular? \$\endgroup\$ – Obada May 11 at 16:22

In your circuit Vc(s) is impressed across each of the 5 branches. You can write a node equation on that top node fairly easily. The current leaving that node in the leftmost branch is Vc(s)/20. Look carefully at the second branch from left and you will see that the current flowing down that branch is [Vc(s) + 1V]/(20+2s). You should be able to work it out from this point.

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  • \$\begingroup\$ If Vl contains both the inductor and the 1V source, would it be correct to put the resistor in between them, and calculate Z(s) = 20 + 2s ?? Or just the fact that they are are in series allows me to do that inspite of Vl being both the inductor and the 1V source together?? \$\endgroup\$ – Obada May 11 at 16:21
  • \$\begingroup\$ Yes, you can find the branch current like I suggest. Once you know that, you can find your VI. \$\endgroup\$ – relayman357 May 11 at 16:29

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