# Thevenin Equivalent of AC RLC Circuit w/ Dependent Voltage

• Engineering
• YellowBelliedMarmot
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.
YellowBelliedMarmot

## Homework Statement

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?

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##.

YellowBelliedMarmot
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!

## 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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