In a transistor, the current amplification factor `alpha` is 0.9. The transistor is connected in common base configuration. The change in collector current when base current changes by 4 mA is

Options

A. 4 mA
B. 12 mA
C. 24 mA
D. 36 mA

Answer

To solve the problem, we need to find the change in collector current (ΔIC) when the base current (ΔIB) changes by 4 mA, given that the current amplification factor (α) is 0.9.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Current amplification factor, α = 0.9
- Change in base current, ΔIB = 4 mA

2. **Understand the Relationship Between α and β:**
- The relationship between α (current gain in common base configuration) and β (current gain in common emitter configuration) is given by the formula:
\[ \beta = \frac{\alpha}{1 - \alpha} \]

3. **Calculate β:**
- Substitute the value of α into the formula:
\[ \beta = \frac{0.9}{1 - 0.9} = \frac{0.9}{0.1} = 9 \]

4. **Use the Relationship Between ΔIC and ΔIB:**
- The relationship between the change in collector current (ΔIC) and the change in base current (ΔIB) is given by:
\[ \Delta I_C = \beta \cdot \Delta I_B \]

5. **Substitute the Values to Find ΔIC:**
- Substitute the calculated value of β and the given value of ΔIB into the equation:
\[ \Delta I_C = 9 \cdot 4 \, \text{mA} = 36 \, \text{mA} \]

6. **Conclusion:**
- The change in collector current (ΔIC) when the base current changes by 4 mA is 36 mA.

### Final Answer:
The change in collector current is **36 mA**.

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