Linear approximation of a nonlinear component.

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SUMMARY

The discussion centers on the effective resistance of a nonlinear resistor (NLR) characterized by the equation IL = gVL² + I0. The user calculates the resistance as R = 1/(2gV0) using the derivative ∂g/∂V at V=V0 but questions the validity of the textbook solution, which states R = 1/2g. The user concludes that the coefficient g has units of amps per volt², leading to the assertion that the textbook answer is incorrect due to dimensional inconsistency.

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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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