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 step by step, we will follow the principles of transistor operation and the relationships between the various currents involved.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The current amplification factor (α) is given as 0.9.
- The change in base current (ΔIb) is given as 4 mA.

2. **Determine the Relationship Between α and β**:
- The relationship between the current amplification factor (α) and the current gain (β) in a transistor 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 change in collector current (ΔIc) can be calculated using the relation:
\[ \Delta Ic = \beta \times \Delta Ib \]
- Substitute the values:
\[ \Delta Ic = 9 \times 4 \text{ mA} = 36 \text{ mA} \]

5. **Final Result**:
- The change in collector current is:
\[ \Delta Ic = 36 \text{ mA} \]

### Summary:
The change in collector current when the base current changes by 4 mA is 36 mA.

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