Loop analysis with complex components

In summary: This is due to the fact that multiplying by -1 changes the sign of both the real and imaginary components.In summary, the conversation discusses finding currents through a circuit using loop analysis and converting complex numbers. The speaker mentions potential errors in the calculations and suggests ignoring certain branch currents and solving for mesh currents first. They also suggest carrying more decimals to avoid rounding errors. The conversation also addresses a potential sign error and how it affects both components of the complex number.
  • #1
geft
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I'm supposed to find the currents flowing through the circuit. While loop analysis is pretty easy, converting a bunch of complex numbers back and forth can get complicated fast. I'm not asking for the exact answer, but please look through the solution to verify if my working is correct. Many thanks.
 

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  • #2
You might have a bit of a problem with the assumed directions of the loop currents versus the branch currents as defined when you write the loop equations. It shows up as an incorrect sign for your I3 value, yielding an incorrect angle.

I usually find it convenient to ignore the "ammeter" branch currents to begin with and solve for the mesh currents. Then go back and calculate the branch currents from them, taking into account their relative directions.

You also might consider carrying another decimal place or two through your intermediate results, as rounding errors are making their way into your first decimal place.
 
  • #3
Many thanks for the feedback. Assuming my calculation is correct, is I1 correct? Can't I3 be fixed by a simple sign change (after converting to rectangular form)?
 
  • #4
geft said:
Many thanks for the feedback. Assuming my calculation is correct, is I1 correct? Can't I3 be fixed by a simple sign change (after converting to rectangular form)?

The sign change will affect both components of the complex number, since the angle has to move from the 1st quadrant to the third quadrant.
 
  • #5
gneill said:
The sign change will affect both components of the complex number, since the angle has to move from the 1st quadrant to the third quadrant.

Why would it affect the magnitude (real component) if you can just add 180° to the phase?
 
  • #6
geft said:
Why would it affect the magnitude (real component) if you can just add 180° to the phase?

It affects the signs of the components.
 

Related to Loop analysis with complex components

1. What is loop analysis with complex components?

Loop analysis with complex components is a method used in electrical engineering to analyze and understand the behavior of circuits with multiple loops and complex components such as capacitors and inductors. It involves applying Kirchhoff's voltage and current laws to determine the voltages and currents at different points in the circuit.

2. Why is loop analysis used with complex components?

Loop analysis is used with complex components because it allows for a more accurate understanding of the behavior of a circuit. The use of complex components can introduce additional variables and complexities that are not present in simple circuits, and loop analysis takes these into account to provide a more complete picture of how the circuit behaves.

3. How is loop analysis with complex components different from other circuit analysis methods?

Loop analysis with complex components differs from other circuit analysis methods such as nodal analysis and mesh analysis in that it specifically focuses on circuits with multiple loops and complex components. It also uses Kirchhoff's voltage and current laws to analyze the circuit, rather than other methods such as superposition or Thevenin's theorem.

4. What are the advantages of using loop analysis with complex components?

There are several advantages to using loop analysis with complex components. First, it can provide a more accurate understanding of the behavior of a circuit with multiple loops and complex components. It also allows for a systematic approach to analyzing the circuit, making it easier to troubleshoot and make changes. Additionally, loop analysis can be used for both AC and DC circuits, making it a versatile tool for circuit analysis.

5. Are there any limitations to using loop analysis with complex components?

While loop analysis with complex components is a powerful tool for circuit analysis, it does have some limitations. It may become more complex and time-consuming to use for circuits with a large number of loops and components, and it may not be suitable for circuits with non-linear components. In these cases, other methods of circuit analysis may be more appropriate.

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