Resistance in case of non Ohmic current voltage relation.

Mitadru Banik

A non Ohmic relation of current and voltage is I=α(exp(eV/kT)-1). Where α,K,T,e are constant. What will be the incremental resistance?

My question is if it don't follow the Ohmic equation then how it possible to find the resistance?

DragonPetter

Incremental resistance refers to small signal resistance. This means that when you take a non-linear load line like the one described by your equation, and vary your position along that line very small by changing the voltage or current respectively small, you will be operating along an -approximate- linear region, since the tangent along this curve at any point is a straight line, which will be an ohmic relation in the sense that it is linearized on this small increment.

Incremental should give you the clue to use a derivative (dV/dI) which is in units of ohms.

Mitadru Banik

Ok understand it but however it never violets the relation V=IR.

NascentOxygen

When speaking of incremental resistance, written as small r, then Ohms Law is written v=i·r
to distinguish 'r' from the DC or large signal resistance seen in V=I·R

Example: If you apply, say, 10 volts DC to an nonlinear resistor and a current flows of 1 ampere, you conclude that that resistor, at 10 volts, seems like a 10 ohm resistor. However, if you increase that 10V to 10.1V and find the current increases to 1.05A, you can say that for small changes near 10V, that resistor appears as a 2 ohm resistor because ∆V/ ∆I = 2Ω.

So at the 10V operating point the resistor simultaneously has two values of resistance, R=10Ω and r=2Ω.

sophiecentaur

Don't worry about that. There is no violation.
It may be better if you don't feel that the 'Resistance' actually has to mean anything, other than V/I. If you don't insist that there must be some physical significance then there is no problem. Likewise, the 'small signal' resistance (ΔV/ΔI) needs to be no more than what it says on the tin.
There are enough really important things to get in a stew about so why worry about what something really 'means'?
One of the first things we have to get over in 'electrics' is to realise that descriptions of Resistance like "It's how hard you need to push electrons through a circuit" are no use to anyone. Resistance is just a RATIO - period.

Mitadru Banik

Thanks to all of u......