# Applying Thevenin's theorem to AC circuits

• Engineering
• mpar3
In summary, the issue in the conversation was about the sign of the imaginary part of a 50 Ω load, which was initially thought to be negative due to a lagging power factor. However, it was clarified that a lagging power factor does not necessarily lead to a negative phase angle, and reference was provided for further understanding.

#### mpar3

Homework Statement
FIGURE 1 shows a 50 Ω load being fed from two voltage sources via
their associated reactances. Determine the current i flowing in the load by:

(a) applying Thévenin’s theorem
(b) applying the superposition theorem
Relevant Equations
Thevenin equivalents, polar & rectangular conversions

So I've seen other threads on here with the same problem from a few years ago, and I'm just not getting the same answers. However, I followed along with a similar problem in the textbook and used all the same methods, so can't understand where I've gone wrong, or if I even am wrong. Also not sure if its ok that the current should be at an angle greater than 90 degrees

arhzz
The Electrician said:
See the first few posts in this thread: https://www.physicsforums.com/threads/thevenins-theorem.775385/

You have the sign of the imaginary part of the 50 Ω load wrong.
I thought a lagging power factor leads to a negative phase angle, and thus a negative imaginary component. Is that not right?

mpar3
The Electrician said:
That is not right.

Part way down the page under the heading "Lagging and leading power factors" you'll find discussion of the topic.
I don't know why I was so set on it being negative. I think I must have mixed it up with the angle between current and voltage maybe. Thanks for your help

## What is Thevenin's theorem?

Thevenin's theorem is a fundamental principle in circuit analysis that states that any linear circuit can be represented by an equivalent circuit with a voltage source, a series resistance, and a load. This allows for simplification of complex circuits and easier analysis.

## How is Thevenin's theorem applied to AC circuits?

Thevenin's theorem can be applied to AC circuits by first converting the circuit to its phasor representation. The voltage source in the equivalent circuit will have the same amplitude and phase as the original circuit, while the series resistance will be the impedance of the original circuit at the load. This allows for analysis of the circuit using familiar AC circuit analysis techniques.

## What are the benefits of using Thevenin's theorem in AC circuit analysis?

Thevenin's theorem allows for simplification of complex AC circuits, making it easier to analyze and understand their behavior. It also allows for the calculation of voltage and current at any point in the circuit without having to solve for the entire circuit. This can save time and effort in circuit design and troubleshooting.

## What are the limitations of Thevenin's theorem?

Thevenin's theorem is only applicable to linear circuits, meaning that it cannot be used for nonlinear circuits such as those containing diodes or transistors. It also assumes that the circuit is in a steady state, meaning that all transients have died out. Additionally, Thevenin's theorem is only accurate for a single frequency and may not accurately represent the behavior of a circuit at different frequencies.

## How can Thevenin's theorem be verified in an AC circuit?

Thevenin's theorem can be verified in an AC circuit by comparing the voltage and current values calculated using the equivalent circuit to those measured in the original circuit. If the values are within an acceptable range of error, the theorem is considered to be valid for that circuit.