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so I'm trying to find the current I(t) passing through the node above the switch. I have already found the DC response of the RC circuit which is

in the form of:

so, after the switch closes a short circuit will be created, and here is the confusion, is the current going to take the shorter path ignoring the 4k resistor and the 12V source and no current will flow through them? with that being said, I don't know whether to consider them in my calculation of I(t) What should I do?

  • \$\begingroup\$ why would you think that the 4 k resistor would have no current flowing through it if you applied 12 V across it? \$\endgroup\$
    – jsotola
    Dec 27 '19 at 20:05
  • \$\begingroup\$ @jsotola I think what he means to say is no part of his current of interest, i(t), flows through the 4k resistor when the switch is closed. \$\endgroup\$
    – DKNguyen
    Dec 27 '19 at 20:29

After the switch closes: You always have to consider everything that will have an effect. In this case, the perfect short basically makes the left and right current loops independent of each other which means that the 12V will no affect the 36V. Write out the loop equations and you will see. There is no component that will have both currents from both halves running through it and therefore no voltage drop is dependent on both loops. And the only thing that carries over from before the switch closes is the cap voltage which is an initial condition.

  • \$\begingroup\$ Should take -1 (I didn't): The 12V loop has big impact on initial voltage of capacitor (while switch is open). \$\endgroup\$ Dec 27 '19 at 19:23
  • \$\begingroup\$ @VillageTech It's not talking about when the switch is open. It's talking about after the switch is closed hence my mention about the perfect short which is also the scenario specifically requested for in the OP's question. \$\endgroup\$
    – DKNguyen
    Dec 27 '19 at 19:27
  • \$\begingroup\$ Yes, but after closing, the I(t) depends on initial conditions. \$\endgroup\$ Dec 27 '19 at 19:30
  • \$\begingroup\$ @VillageTech And? I already covered that. Are you getting confused because the first paragraph talks about when the switch is open and the second paragraph talks about when the switch is closed? \$\endgroup\$
    – DKNguyen
    Dec 27 '19 at 19:31
  • 1
    \$\begingroup\$ @VillageTech I'll try and clarify it. \$\endgroup\$
    – DKNguyen
    Dec 27 '19 at 19:33

You have an equation for the voltage across the capacitor as a function of time. After the switch closes, the 6kΩ resistor is in parallel with the capacitor. That should be enough information for you to find \$i(t)\$

  • \$\begingroup\$ thank you... :) \$\endgroup\$
    – Obada
    Dec 27 '19 at 21:18

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