Are My Superposition Circuit Equations Correct?

In summary, the author is trying to solve a circuit with three current sources, one voltage source, and one resistor. He is having difficulty finding the current source and is wondering if he is doing it correctly.
  • #1
gomezfx
20
0

Homework Statement


Find v0 and i0
[PLAIN]http://img214.imageshack.us/img214/2051/superquestion.jpg

Homework Equations


KVL and KCL

The Attempt at a Solution


I removed the voltage source and redrew the circuit with a short on the bottom left. I then used mesh current analysis with KVL and made a system of equations. My problem is that all of my current (i0, i1, i2, i3) come out to 0 which is definitely wrong.

Am I approaching this problem correctly and setting up my equations right?

my work:
http://img530.imageshack.us/img530/4779/superosition.jpg
 
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  • #2
Looks like your on the right track! :)
 
  • #3
With the 180 V source shorted, call the current through the 60 ohm resistor i1 (upward). Then the sum of the voltages around the loop on the lower left is 60i1 + 30(i1 + 7.5) = 0. This yields i1 = -2.5A straightaway. You can actually see that without the equations - clearly 2/3 of the current will go through the 30 ohm resistor and 1/3 through the 60. Looks like you forgot to use the 7.5 amps in that loop, and in the others. Very tough to find i0 . . .
 
  • #4
To solve the circuit by super position method, you should not close the voltage source and open the current source. Keep them as it is and apply KVL and XCL.
 
  • #5
Delphi51 said:
With the 180 V source shorted, call the current through the 60 ohm resistor i1 (upward). Then the sum of the voltages around the loop on the lower left is 60i1 + 30(i1 + 7.5) = 0. This yields i1 = -2.5A straightaway. You can actually see that without the equations - clearly 2/3 of the current will go through the 30 ohm resistor and 1/3 through the 60. Looks like you forgot to use the 7.5 amps in that loop, and in the others. Very tough to find i0 . . .

I'm having a hard time understanding this, is my circuit drawing correct? Because isn't the 60 not just i1?, isn't it 60(i1-i0)?
 
  • #6
rl.bhat said:
To solve the circuit by super position method, you should not close the voltage source and open the current source. Keep them as it is and apply KVL and XCL.

Isn't that what the superposition method is though? Closing independent sources and solving circuits with only one source at a time.

So don't I need two separate circuits with only a current source or a voltage source?
 
  • #7
gomezfx said:
Isn't that what the superposition method is though? Closing independent sources and solving circuits with only one source at a time.

So don't I need two separate circuits with only a current source or a voltage source?

Not necessarily. Superposition method involves asigning a current in each loop and applying KVL.
 
  • #8
rl.bhat said:
Not necessarily. Superposition method involves asigning a current in each loop and applying KVL.

So I should just try solving the circuit as given originally?
 
  • #9
You have to be extremely careful about defining i1. I defined it as the current through the 60 ohm resistor because I thought your i1 loop on the diagram was ambiguous.

There is an example of the superposition method here:
http://circuits.solved-problems.com/936/superposition-problem-voltage-current-sources/#more-936

Here is an article on doing it without superposition:
http://en.wikipedia.org/wiki/Mesh_analysis
I'm sure rl.bhat knows a great deal more about this than I do!
 
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FAQ: Are My Superposition Circuit Equations Correct?

What is a superposition circuit problem?

A superposition circuit problem is a type of problem in electrical engineering and physics that involves analyzing the behavior of a circuit with multiple input sources. It relies on the principle of superposition, which states that the total response of a linear system is equal to the sum of the individual responses to each input source.

How is superposition used to solve circuit problems?

Superposition is used to solve circuit problems by breaking down the circuit into smaller parts and analyzing each part separately. The individual responses from each part are then combined to determine the overall response of the circuit.

What are the limitations of using superposition to solve circuit problems?

One limitation of using superposition to solve circuit problems is that it only applies to linear circuits, meaning that the components in the circuit must follow Ohm's law. Additionally, it cannot be used for circuits with dependent sources.

How do you determine which input source is active in a superposition circuit problem?

To determine which input source is active in a superposition circuit problem, you can use the principle of superposition to analyze each input source separately. The active source is the one being analyzed while the other sources are set to zero or replaced with their internal resistance.

Are there any real-life applications of superposition circuits?

Yes, superposition circuits have many real-life applications in fields such as electronics, telecommunications, and power systems. For example, in telecommunications, superposition is used to analyze the different signals in a communication channel, and in power systems, it is used to calculate the voltage and current in different branches of a complex network.

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