Linear approximation of a nonlinear component.

AI Thread Summary
The discussion focuses on finding the effective resistance of a nonlinear resistor (NLR) using linear approximation techniques. The user calculates resistance as R = 1/(2gV0) but questions why it differs from the textbook solution of 1/2g. Clarification is sought on whether V0 should be determined first before substituting it into the equation. Additionally, concerns are raised about the units of the coefficient g, which do not align with standard resistance units. The conclusion suggests that the textbook answer may be incorrect based on the unit analysis provided.
peripatein
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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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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.
 

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