Thevenin Equivalent of AC RLC Circuit w/ Dependent Voltage

In summary, to find Vth and Zth for a circuit with only dependent voltage sources and a frequency of 2 kHz, one can use nodal analysis and add a generic 2 kHz current source at the load terminals. Solving for vab and dividing it by the current source will give the desired impedance.
  • #1
YellowBelliedMarmot
10
1

Homework Statement


Diagram.png

Find Vth and Zth.
frequency = 2kHz

Homework Equations


w = 2 * (pi) * f
ZL = j w L
ZC = -j / (w * C)
V = I*Z
ZR = R

The Attempt at a Solution


At first I tried using nodal analysis which I receive the value V = 0 v. I believe this is because this circuit only has dependent voltage sources. Therefore, the Vth is just 0 v.

10mH ---> j125.7
1uF ---> -j79.6
100 ohms ---> 100
w = 2*(pi)*2000 = 12566.37

Essentially, I am stuck. I have some theories as to what I can do though. I remember from DC circuit analysis that we can either add a 1v or a 1A (the number is arbitrary) source between terminals a and b, but I'm not sure what to do beyond that. Could I add a 1A (i.e. 1*cos(wt)) between the terminals, and then do nodal analysis? Then after that, would I take that voltage and divide it by the 1A (1cos(wt)) AC source to get the Zth? And as I mentioned above, wouldn't the thevenin equivalent of this circuit not even have a Vth since there's no independent sources?
 
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  • #2
A zero value for the Thevenin voltage is reasonable; zero is a perfectly good real number.

For the impedance, your suggested approach has merit: add a generic 2 kHz current source ##I## at the load terminals. Use nodal analysis again leaving that current source as a variable and solve for ##v_{ab}##. Note that the desired impedance is ##v_{ab} / I##.
 
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  • #3
gneill said:
A zero value for the Thevenin voltage is reasonable; zero is a perfectly good real number.

For the impedance, your suggested approach has merit: add a generic 2 kHz current source ##I## at the load terminals. Use nodal analysis again leaving that current source as a variable and solve for ##v_{ab}##. Note that the desired impedance is ##v_{ab} / I##.
I tried it out and it worked! Thanks for your help! All this circuit stuff is starting to really make sense now!
 

Related to Thevenin Equivalent of AC RLC Circuit w/ Dependent Voltage

What is the Thevenin Equivalent of an AC RLC Circuit with Dependent Voltage?

The Thevenin Equivalent of an AC RLC Circuit with Dependent Voltage is a simplified circuit representation that consists of a single voltage source and a single impedance. It is used to analyze the behavior of a complex circuit and calculate the voltage across a specific load.

How is the Thevenin Equivalent Voltage Calculated?

The Thevenin Equivalent Voltage is calculated by open-circuiting the load and finding the voltage across the load terminals. This voltage is the Thevenin Equivalent Voltage.

What is the Difference Between Thevenin and Norton Equivalent Circuits?

The main difference between Thevenin and Norton Equivalent Circuits is the representation of the circuit. Thevenin Equivalent uses a voltage source and impedance, while Norton Equivalent uses a current source and impedance. They both provide the same information about the circuit, but one may be more convenient to use depending on the analysis being performed.

How is the Thevenin Equivalent Impedance Calculated?

The Thevenin Equivalent Impedance is calculated by short-circuiting the load and finding the impedance across the load terminals. This impedance is the Thevenin Equivalent Impedance and can be used to calculate the current through the load.

Why is the Thevenin Equivalent Circuit Useful?

The Thevenin Equivalent Circuit is useful because it simplifies a complex circuit into a single voltage source and impedance. This makes it easier to analyze the circuit and calculate the voltage across a specific load without having to consider the entire circuit. It also allows for the replacement of a complex circuit with a simpler one, which can save time and resources in circuit design and troubleshooting.

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