How Do You Determine Thevenin Equivalent Circuits and Maximize Power Transfer?

In summary, the conversation discusses finding the Thevenin equivalent circuit for a given circuit. The steps involve finding the open circuit voltage (VOC) and using the test source method to determine the Thevenin resistance. This is then used to find the load resistor that results in maximum power transfer. The use of a test voltage source versus a test current source is also discussed. The conversation also includes a mistake made in using node voltage analysis, where the controlled source was not accounted for in the equation.
  • #1
jdawg
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2

Homework Statement



Find the Thevenin equivalent circuit for the circuit shown. You will need to find VOC and then use the test source method to find the Thevenin resistance. Using the Thevenin equivalent circuit,determine the load resistor that results in maximum power transferred to that load resistor and the amount of that power.

Homework Equations

The Attempt at a Solution


(Fig.1)[/B]I'm a little stuck on this problem. I first used mesh analysis to find VOC, which came out correct: VOC=2.5V.
But I tried to do it with node voltage analysis as well to see if it would work also and it came out a little messed up:
(VA-5)/7 +VA/10=0
VA=2.94V
Is there a reason why node voltage doesn't work in this situation or am I just doing it wrong?
(Fig.2) I tried letting ITest=1A and used mesh analysis:
i2=ITest=1
0.2(V2)-(5ohm)(i1)+5v-(7ohm)(i1)-(10ohm)(i1-i2)=0
Substituted and did some algebra:
i1=0.705
I am super confused at this point :(
Is there an advantage to using a test voltage source vs using a test current source?
Should I have let VTest=2.5V instead?
 

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  • #2
Oops I forgot to take out the independent voltage source for the test method! I let Vtest=2.5v and found Itest=0.467 so Rth=6ohms! I feel like I understand the test method now, could someone explain how I messed up with the node voltage equation in the Fig. 1 section?
 
  • #3
jdawg said:
Oops I forgot to take out the independent voltage source for the test method! I let Vtest=2.5v and found Itest=0.467 so Rth=6ohms! I feel like I understand the test method now, could someone explain how I messed up with the node voltage equation in the Fig. 1 section?
You didn't account for the controlled source in the node equation. You need all sources active if you want to find the open circuit voltage.
 
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Thanks!
 

What is a Thevenin equivalent circuit?

A Thevenin equivalent circuit is a simplified representation of a complex electrical circuit. It consists of a voltage source in series with a resistor, and is used to model the behavior of a circuit at a specific point or load.

How is a Thevenin equivalent circuit calculated?

To calculate a Thevenin equivalent circuit, you must determine the open-circuit voltage (VOC) and the equivalent resistance (Req) at the load. VOC is the voltage across the load when there is no current flowing, and Req is the resistance of the circuit as seen from the load terminals. VOC can be calculated using Kirchhoff's voltage law, and Req can be found using Ohm's law.

When is a Thevenin equivalent circuit useful?

A Thevenin equivalent circuit is useful in analyzing complex circuits, as it simplifies the circuit to a single voltage source and resistor. This makes it easier to calculate and understand the behavior of the circuit at a specific point or load. It is also helpful in circuit design, as it can aid in selecting the appropriate components for a given application.

What are the limitations of a Thevenin equivalent circuit?

A Thevenin equivalent circuit is only accurate for linear circuits, meaning that the relationship between voltage and current in the circuit must follow Ohm's law. It also assumes that the load is connected to the circuit terminals, and that the load does not change the behavior of the circuit. Additionally, it does not account for non-idealities such as temperature effects or component tolerances.

How does a Thevenin equivalent circuit differ from a Norton equivalent circuit?

A Norton equivalent circuit is similar to a Thevenin equivalent circuit, but uses a current source in parallel with a resistor instead of a voltage source in series with a resistor. While a Thevenin equivalent circuit is more commonly used in circuit analysis, a Norton equivalent circuit may be preferred in certain situations, such as when the load is better modeled as a current-driven device.

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