### Mathematical Expression for the Dynamic Resistance

We have seen that the dynamic resistance is the reciprocal of the slope of the V-I characteristic of a diode. For the incremental changes in voltage and current we have write,
Now current equation of a diode is given by,
But from the current equation we can write,
Substituting in equation (3), we get,
While determining the value of dynamic resistance under forward biased and reverse biased conditions, the general expression, equation (3) is used.
Note : For forward biased condition treat V positive while for revers biased condition treat V as negative, while using the expression.
Example : For a germanium diode, the reverse saturation current is 2 μA at a reverse voltage of 0.26 V. Calculate forward and reverse dynamic resistance values if forward biased voltage is also 0.26 V, at room temperature.
Solution : The given values are
I= 2 μA,  V = + 0.26 V   for forward biased, V = -0.26 V  for reversed biased.
η = 1 for germanium,  VT = 26 mV at room temperature.

= 0.5901 Ω  Forward dynamic resistance

= 286.34 MΩ   Reverse dynamic resistance