The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure.

The estimated current gain from the figure is ___.

Upon reviewing the mathematical syntax in the previous derivation, a formatting error was found where the fraction line failed to render properly under Section 3. Here is the fully corrected, clean solution:

1. Understand the Core Formula

In a common-emitter transistor configuration, the AC current gain ($$\beta_{\text{ac}}$$) is defined as the ratio of the change in collector current ($$\Delta I_c$$) to the change in base current ($$\Delta I_b$$) at a constant collector-emitter voltage ($$V_{CE}$$):

$$\beta = \left( \frac{\Delta I_c}{\Delta I_b} \right)_{V_{CE}}$$

2. Extract Data Points from the Graph

Looking at the linear region of the output characteristics curve , we can select two adjacent steady curves to calculate the differences:

• At $$I_{B1} = 20\ \mu\text{A}$$, the corresponding collector current is $$I_{c1} = 4\text{ mA}$$.
• At $$I_{B2} = 30\ \mu\text{A}$$, the corresponding collector current is $$I_{c2} = 6\text{ mA}$$.

3. Calculate the Current Gain ($$\beta$$)

Let's find the values for the change in both currents:

• $$\Delta I_c = 6\text{ mA} - 4\text{ mA} = 2\text{ mA} = 2 \times 10^{-3}\text{ A}$$
• $$\Delta I_b = 30\ \mu\text{A} - 20\ \mu\text{A} = 10\ \mu\text{A} = 10 \times 10^{-6}\text{ A}$$

Substitute these values back into our current gain ratio:

$$\beta = \frac{2 \times 10^{-3}}{10 \times 10^{-6}}$$

$$\beta = \frac{2}{10} \times 10^3 = 0.2 \times 1000 = 200$$

Conclusion

The estimated current gain from the figure is 200.