Register to reply 
Linear approximation of a nonlinear component. 
Share this thread: 
#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: 5,365

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. 


Register to reply 
Related Discussions  
Linear & nonlinear shooting and linear & nonlinear finite difference methods  Calculus & Beyond Homework  0  
ODE (linear vs. nonlinear)  Calculus & Beyond Homework  1  
Linear vs Nonlinear  Calculus & Beyond Homework  1  
Radial component of linear acceleration  Introductory Physics Homework  6  
Linear Approximation  Introductory Physics Homework  3 