Linear approximation of a nonlinear component.

[peripatein]

Hello,
I am trying to find the effective resistance of the NLR in the attachment (to the first order). It is given that I_L = gV_L² + 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.

 

[NascentOxygen]

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.