Ohm's Law — Question 9

Question 9

A threshold device has an ohmic branch without an ohmic full characteristic

An idealized device obeys $I=0$ for $|V|\le V_t$, and $I=[V-\operatorname{sgn}(V)V_t]/R$ for $|V|>V_t$, with $V_t,R>0$.

1. At $V=2V_t$, find static and differential resistance.

2. Find the current at $V=V_t/2$ and assess whether a single resistance models all operating points.

Question 9 - Solution

A threshold device has an ohmic branch without an ohmic full characteristic

(a) Method and calculation

$$I(2V_t)=V_t/R,\quad R_s=2V_t/(V_t/R)=2R.$$$$r_d=(dI/dV)^{-1}=R\quad\text{on the conducting branch}.$$

(b) Interpretation and further calculation

$$I(V_t/2)=0,\quad V/I\ \text{is not finite there}.$$$$I(V)=V/R_{\mathrm{constant}}\ \text{cannot reproduce both regimes}.$$

Physical check

The differential resistance is undefined at the ideal sharp threshold itself; results above avoid that point.