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.
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.
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.