Solving Circuit with Superposition Theorem

In summary, the conversation discusses a problem involving a circuit and finding the current through the R2 branch. The approach involves combining parallel resistors and using the superposition principle. The question of whether R1 and XL are in parallel is discussed, and the use of the product sum rule is suggested. The conversation also mentions using a voltage divider formula to find the current total for the first source through branch R2, and the concept of superposition is reiterated.
  • #1
Jason03
161
0
I was working on this circuit.

http://img404.imageshack.us/img404/3537/imptm6.jpg

The problem asks to find the current through the R2 branch...

Heres my approach and questions...

Start from the opposite end of the circuit...combine the 2 parallel resistors R2 and R3...the V2 goes to zero because of the superposition...

The only question I had was are R1 and XL in parallel?...if so I could combine the R2 and R3 total found with R1..using product sum rule...

Finally add XC to (XL)(R1)/(XL + R1)...to get the total impedence

than from there find the current...(current divider)
 
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  • #2
Jason03 said:
I was working on this circuit.

http://img404.imageshack.us/img404/3537/imptm6.jpg

The problem asks to find the current through the R2 branch...

Heres my approach and questions...

Start from the opposite end of the circuit...combine the 2 parallel resistors R2 and R3...the V2 goes to zero because of the superposition...

The only question I had was are R1 and XL in parallel?...if so I could combine the R2 and R3 total found with R1..using product sum rule...

Finally add XC to (XL)(R1)/(XL + R1)...to get the total impedence

than from there find the current...(current divider)

When determining the contribution of V1, R1 and XL are not in parallel, however, XL *is* in parallel with (R1+R2//R3). This combined resistance is then in series with XC. Unless you want to do a source transform on V1 to get a current divider.

Here's the secret to source transform (or any circuit analysis, for that matter): draw, redraw, and redraw circuits (after every transformation / simplification). Unless you can get to the point where you can just do things by inspection. Also, learn to draw things neatly, otherwise, it won't be worth all the extra paper.

EDIT: You don't mention this explicitly in your post, so I'll assume you've determined the contribution of V2 in the absence of V1...
 
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  • #3
ok thanks...now I understand that part...

I calculated Z total for the first source...now to find the current total for the first source only through branch R2...I know I can use the voltage divider formula...but I don't remember how...

I know I have to find the relationships between the branches (except R2)...multiply..divide...and multiply that total by the current total already found...

I just don't remember how to apply the voltage divider formula correctly...

( I started finding Z for source 2 and it appears to be the same as source 1?...is that correct?.,...the difference would be in finding the current considering the sources are at different voltages and phases..)
 
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  • #4
Jason03 said:
ok thanks...now I understand that part...

I calculated Z total for the first source...now to find the current total for the first source only through branch R2...I know I can use the voltage divider formula...but I don't remember how...

I know I have to find the relationships between the branches (except R2)...multiply..divide...and multiply that total by the current total already found...

I just don't remember how to apply the voltage divider formula correctly...

( I started finding Z for source 2 and it appears to be the same as source 1?...is that correct?.,...the difference would be in finding the current considering the sources are at different voltages and phases..)

You need a formula for voltage divider?! :-D The ratio of the potential drop in two resistors (impedances) is the same as the ratio of their resistances (impedances). Or, V_drop_Z1 = V_source*Z1/(Z1+Z2). Remember, that's just the voltage DROP, not necessarily the nodal voltage measured relative to ground (or another reference). See other threads in this forum on that topic if you're still stuck...

Regarding your other point, superposition says that it's okay if the sources are at different voltages and phases. Their individual contributions just add up (superpose) and the total is what you actually measure when you hook up your oscilloscope.
 

1. How does the Superposition Theorem work in circuit analysis?

The Superposition Theorem is a method used to solve complex circuits by breaking them down into simpler, individual circuits. This is done by considering one source at a time and then summing the results to get the overall solution. By isolating each source, the calculation becomes easier and more manageable.

2. What are the limitations of using the Superposition Theorem?

The Superposition Theorem can only be applied to linear circuits, meaning that the components in the circuit must follow Ohm's law and have a linear relationship between voltage and current. Additionally, all sources must be independent and cannot be affected by other sources or components in the circuit.

3. How do I determine which sources to consider when applying the Superposition Theorem?

To apply the Superposition Theorem, each source in the circuit must be considered one at a time while all other sources are turned off. This means that voltage sources are replaced with a short circuit and current sources are replaced with an open circuit. The resulting circuit is then solved for the desired variable.

4. Can the Superposition Theorem be used for circuits with multiple dependent sources?

Yes, the Superposition Theorem can be applied to circuits with multiple dependent sources. The process is the same as with independent sources, where one source is considered at a time while the others are turned off. However, the dependent sources must remain in the circuit and the resulting equations will include their values.

5. Are there any other methods for solving complex circuits besides the Superposition Theorem?

Yes, there are other methods such as Kirchhoff's laws, nodal analysis, and mesh analysis. Each method has its own advantages and limitations, and the choice of method will depend on the type of circuit and the desired solution. It is important to understand and be familiar with multiple methods for circuit analysis in order to choose the most efficient and accurate approach for a given problem.

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