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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.


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.

  • \$\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

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.


simulate this circuit – Schematic created using CircuitLab

  • 1
    \$\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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