Ohm's Law — Question 3

Question 3

Two operating points identify the onset of nonohmic response

A device follows $I=GV+\beta V^3$. At V=1.00 V its current is 3.00 mA; at V=2.00 V it is 12.0 mA. Temperature is held constant.

1. Infer G and beta.

2. Find the nonzero voltage magnitude at which the cubic current equals the linear current, and the differential conductance there.

Question 3 - Solution

Two operating points identify the onset of nonohmic response

(a) Method and calculation

$$G+\beta(1\,\mathrm V)^2=3.00\,\mathrm{mS},\quad G+\beta(2\,\mathrm V)^2=6.00\,\mathrm{mS}.$$$$G=2.00\,\mathrm{mS},\quad\beta=1.00\,\mathrm{mA/V^3}.$$

(b) Interpretation and further calculation

$$\beta V_*^3=GV_*\Rightarrow |V_*|=\sqrt{G/\beta}=\sqrt2\,\mathrm V.$$$$g_d=G+3\beta V_*^2=4G=8.00\,\mathrm{mS}.$$

Physical check

The extra current cannot be explained by a single constant resistance at both operating points.