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Linear approximation of a nonlinear component. 
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#1
Jul1813, 11:59 AM

P: 818

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_{L}^{2} + I_{0}. I understand that this is normally achieved via ∂g/∂V at V=V_{0}, but when I do so I get that R should be 1/(2gV_{0}), 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 V_{0} and then substitute it in 1/(2gV_{0})? But then, for my solution to be the same as that in the attachment, won't V_{0} have to be 1? I'd sincerely appreciate some guidance. 


#2
Jul1913, 09:01 AM

HW Helper
Thanks
P: 5,166

Your equation indicates that the coefficient g has units of amps per volt^{2}
The reciprocal of this must have units of volt^{2} per ampere. This is not Ohms, nor Ohms^{1}. Therefore, the text book answer cannot be correct. 


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