Linear approximation of a nonlinear component.

In summary, the conversation is about finding the effective resistance of the NLR in the attachment. The person is trying to use ∂g/∂V at V=V0 to find the resistance, but their calculation does not match the solution. They are wondering if they should determine V0 first and then substitute it in, but this would not result in the same answer as the textbook.
  • #1
peripatein
880
0
Hello,
I am trying to find the effective resistance of the NLR in the attachment (to the first order). It is given that IL = gVL2 + I0. I understand that this is normally achieved via ∂g/∂V at V=V0, but when I do so I get that R should be 1/(2gV0), and not 1/2g as shown in the solution. Could anyone please explain to me what it is I am doing wrong? Ought I to first determine V0 and then substitute it in 1/(2gV0)? But then, for my solution to be the same as that in the attachment, won't V0 have to be 1? I'd sincerely appreciate some guidance.
 

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  • #2
Your equation indicates that the coefficient g has units of amps per volt2
The reciprocal of this must have units of volt2 per ampere. This is not Ohms, nor Ohms-1.

Therefore, the textbook answer cannot be correct.
 

What is linear approximation?

Linear approximation is a mathematical technique used to approximate the behavior of a nonlinear component or function by using a linear equation. It is often used in engineering and science to simplify complex systems and make them easier to analyze.

Why do we use linear approximation?

Linear approximation is useful because it allows us to approximate the behavior of nonlinear components or functions without having to solve complicated equations. This can save time and make it easier to understand the overall behavior of a system.

How is linear approximation calculated?

Linear approximation is calculated by finding the tangent line to a nonlinear function at a certain point. The slope of this tangent line is equivalent to the derivative of the function at that point. The linear equation is then formed using this slope and the point of tangency.

What are the limitations of linear approximation?

Linear approximation is only accurate for small changes around the point of approximation. As the distance from this point increases, the accuracy of the linear approximation decreases. Additionally, linear approximation may not accurately capture the behavior of a system if there are significant nonlinearities present.

What are some real-world applications of linear approximation?

Linear approximation is commonly used in engineering, physics, and economics. It can be applied to predict the behavior of systems such as electrical circuits, chemical reactions, and population growth. It is also used in financial modeling and data analysis.

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