The $V-I$ characteristic of a silicon diode is shown in the Figure. Calculate the resistance of the diode at $(a) \; I_{D} = 15 \, mA$ and $(b) \; V_{D} = -10 \, V$.

(N/A) To calculate the resistance of the diode,we use Ohm's law,$R = V / I$ or $r = \Delta V / \Delta I$.
$(a)$ For the forward bias region,we calculate the dynamic resistance at $I_{D} = 15 \, mA$. From the graph,we can take the slope between $I = 10 \, mA$ $(V = 0.7 \, V)$ and $I = 20 \, mA$ $(V = 0.8 \, V)$.
$r_{f} = \Delta V / \Delta I = (0.8 \, V - 0.7 \, V) / (20 \, mA - 10 \, mA) = 0.1 \, V / 10 \, mA = 10 \, \Omega$.
$(b)$ For the reverse bias region at $V_{D} = -10 \, V$,the current is $I = -1 \, \mu A$.
The static resistance is $r_{r} = |V| / |I| = 10 \, V / 1 \, \mu A = 10 \, V / (1 \times 10^{-6} \, A) = 1.0 \times 10^{7} \, \Omega$.