Question

calculate the dynamic slope resistance when a voltage of 50V is applied across a germanium diode at 300K when saturation current is 10uA

Answer 1

The current is

$$I=I_s(e^{\frac{qV}{kT}}-1).$$

The dynamic resistance is

$$r_{ac}=\frac{kT}{qI}=\frac{kT}{qI_s(e^{\frac{qV}{kT}}-1)},\\\space\\ r_{ac}=\frac{(1.38\cdot10^{-23})300}{(1.6\cdot10^{-19})(10\cdot10^{-6})(2.72^{\frac{(1.6\cdot10^{-19})50}{(1.38\cdot10^{-23})300}}-1)}=0.$$

The reason for such a small resistance is the value of voltage of 50 V. Typically the value is less than 1 volt.