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Confused on how to handle a dependent source in an RLC parallel circuit. This questions asks me to find the function that describes v(t) and hints that it is an over damped system.

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Confused on how to handle a dependent source in an RLC parallel circuit

This answer mistakenly saw the current controlled voltage source as a current controlled current source so apologies on that and thanks to stretch for pointing y blindness out. I should have realized when R2 didn't come into things. It's the same hint with a hint of a modification.

Hint: -

Start with the voltage source of 80 volts in series with R1. Convert this to a current source in parallel with R1. Now parallel that with the 80i current source. Now you have two current sources in parallel that are additive and hence combine into a single current source in parallel with R1.

I reckon the combined current source has a value of 25.92 amps (80x81/250). Finally, convert back to a voltage source in series with R1. I reckon the voltage source is 6480 volts.

So now you have got rid of the dependent source and replaced it and the 80 volt source with a single voltage in series with a resistor.

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  • \$\begingroup\$ The dependent source is a current controlled voltage source. \$\endgroup\$ – stretch Feb 24 '17 at 13:21
  • \$\begingroup\$ @stretch oops. I was never any good on these symbols. OK the thing to do is convert that to a current source in parallel with R2 then add the two current sources and convert to a voltage source using R1 and R2. Basically it's the same methodology. \$\endgroup\$ – Andy aka Feb 24 '17 at 14:57
  • \$\begingroup\$ I had to look up the symbol. As luck would have it, CircuitLab had it. Like you, I was puzzled by the 80 ohms, and that's what made me look. It's also in Wikipedia. \$\endgroup\$ – stretch Feb 24 '17 at 16:38
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The hangup is mostly intuitive, I think. Calculating the Thevenin equivalent of all the circuitry left of the switch is straightforward but seems funny. You're interested in finding, first, a circuit with the same open circuit voltage. i in that case flows backwards through the dependent source. The loop current is 195 ma. and Voc is 31.2. Then you want to find the short circuit current. It's 80/250 from the left source and resistor, plus (80/250 * 80)/80 from the right (dependent) source and 80 ohm resistor: 640 milliamps total. Solving for the equivalent resistance: 31.2/.64 = 48.8 ohms.

schematic

simulate this circuit – Schematic created using CircuitLab

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    \$\begingroup\$ When there is no load, the dependent voltage source still has a voltage, therefore the open circuit voltage Vth is not 80V. \$\endgroup\$ – rioraxe Feb 25 '17 at 1:32
  • \$\begingroup\$ @rioraxe I'm not sure it's exactly what you meant, but the values are wrong. I assumed that current flowing backwards through the dependent source would cause its voltage to oppose/stop it. Faulty intuition. I corrected the answer. \$\endgroup\$ – stretch Mar 3 '17 at 14:26

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