Using the superposition principle

In summary, the superposition principle is used to find the current in a circuit by considering each source separately. For i1, the 12V and 4A sources are neglected and the current is found to be 1A. For i2, the 16V and 4A sources are neglected and the current is found to be -0.75A. To find i3, the 4A current source is split between the 2 ohm and 14 ohm branches, with a ratio of 7:1, giving a final current of 0.75A.
  • #1
Edwardo_Elric
101
0

Homework Statement


Find I in the circuit using the superposition principle
Circuit1.jpg

Homework Equations


superposition:
I = i_1 + i_2 + i_3

The Attempt at a Solution


for i_1 we neglect the 12V and the 4A sources:
(8 + 2 + 6)i_1 - 16 = 0
i_1 = 1A

for i_2 we neglect the 16V and the 4A sources:
(8 + 2 + 6)i_2 + 12 = 0
i_2 = -0.75

i don't actually know how to solve for the current in i_3:
Circuit2.jpg

since there are two nodes only i use parallel resistors:
6 + 8 = 14ohms... and 2 ohms are parallel
1/14 + 1/2 = 1/R
R = 1.75
current source = 4 A
so the current source and 1.75 are in parallel... so what i need is to solve the outer current,i_3
now I am really stuck can someone help pls
ans. I = 0.75A
 
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  • #2
Is there a diagram or anything? May be helpful, at least for me.
 
  • #3
lukas86 said:
Is there a diagram or anything? May be helpful, at least for me.

what kind of diagram?
it is already shown: outer current of parallel(2 ohm and 4A) is required
 
  • #4
Hi Edwardo Elric,

You almost have the current for i3. You know that the 4A is splitting, with part of it going to the 2 ohm branch, and part going to the 14 ohm branch. Now the question is, if that is true, how much of the 4A goes in the 14ohm branch? That is i3.

You can find it by considering that since the ratios of the resistances are 1:7, the ratio of the currents must be 7:1. Do you get the answer?
 

1. What is the superposition principle?

The superposition principle is a mathematical concept that states that the total response of a system is equal to the sum of the individual responses from each input. This means that if you have multiple inputs acting on a system, the resulting response can be calculated by adding the responses of each input separately.

2. How is the superposition principle used in science?

The superposition principle is used in many scientific fields, such as physics, engineering, and chemistry. It is particularly useful in analyzing complex systems that have multiple inputs or factors that contribute to the overall response. By breaking down the system into smaller, individual components, scientists can use the superposition principle to understand how each input affects the overall response.

3. Can the superposition principle be applied to all types of systems?

In theory, the superposition principle can be applied to any linear system, meaning that the output is directly proportional to the input. This includes mechanical, electrical, and acoustic systems. However, there are some non-linear systems where the principle may not apply.

4. How is the superposition principle different from other mathematical principles?

The superposition principle is different from other mathematical principles because it allows for the analysis of complex systems without having to solve the entire system at once. Other principles, such as the principle of mathematical induction or the Pythagorean theorem, focus on solving specific problems or equations. The superposition principle, on the other hand, is a general concept that can be applied to a wide range of systems and problems.

5. Are there any limitations to using the superposition principle?

While the superposition principle is a useful tool in many scientific applications, it does have some limitations. As mentioned earlier, it may not apply to non-linear systems. Additionally, it assumes that the individual responses from each input are independent of each other, which may not always be the case in real-world scenarios. It is important for scientists to carefully consider the limitations and assumptions of the superposition principle when applying it to a particular system or problem.

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