For the forward biased diode characteristics shown in the figure, the dynamic resistance at $$I_D = 3$$ mA will be ___ $$\Omega$$.

We need to determine the dynamic resistance of the forward-biased diode at a diode current of $$I_D = 3\text{ mA}$$ using the provided characteristic curve.

1. Understand the Concept of Dynamic Resistance

Dynamic (or AC) resistance ($$r_d$$) of a diode represents its resistance under alternating current conditions. Unlike static resistance ($$V/I$$), dynamic resistance is defined as the reciprocal of the slope of the forward $$I\text{-}V$$ characteristic curve at that specific operating point:

$$r_d = \frac{\Delta V_D}{\Delta I_D}$$

Where $$\Delta V_D$$ is the change in diode voltage and $$\Delta I_D$$ is the corresponding change in diode current along the linear operating region.

2. Extract Data Points from the Graph

Looking at the linear portion of the forward characteristics passing through the region around $$I_D = 3\text{ mA}$$, we can identify two clear reference coordinate points $$(V_D, I_D)$$ on the grid lines:

• Point 1: When $$V_{D1} = 0.7\text{ V}$$, the current is $$I_{D1} = 1\text{ mA}$$  $$\implies (0.7\text{ V}, 1\text{ mA})$$
• Point 2: When $$V_{D2} = 0.8\text{ V}$$, the current is $$I_{D2} = 5\text{ mA}$$  $$\implies (0.8\text{ V}, 5\text{ mA})$$

3. Calculate the Changes ($$\Delta V_D$$ and $$\Delta I_D$$)

Now, compute the differences between these two operating states along the straight line segment:

$$\Delta V_D = V_{D2} - V_{D1} = 0.8\text{ V} - 0.7\text{ V} = 0.1\text{ V}$$

$$\Delta I_D = I_{D2} - I_{D1} = 5\text{ mA} - 1\text{ mA} = 4\text{ mA} = 4 \times 10^{-3}\text{ A}$$

4. Calculate the Dynamic Resistance ($$r_d$$)

Substitute the voltage change and current change values back into our main dynamic resistance formula:

$$r_d = \frac{0.1\text{ V}}{4 \times 10^{-3}\text{ A}}$$

$$r_d = \frac{0.1 \times 10^3}{4} = \frac{100}{4} = 25\ \Omega$$

Final Answer: $$25$$