The current amplification factor `alpha` of a common base transistor and the current amplification factor `beta`of a common emitter transistor are not related by

Options

A. `alpha=beta/(1+beta)`
B. `beta=alpha/(1-alpha)`
C. `1/alpha-1/beta=1`
D. `beta=alpha/(1+alpha)`

Explanation

To solve the problem regarding the relationship between the current amplification factors `alpha` (α) of a common base transistor and `beta` (β) of a common emitter transistor, we need to analyze the definitions and relationships of these parameters.

### Step-by-Step Solution:

1. **Understand Definitions**:
- The current amplification factor `alpha` (α) for a common base configuration is defined as:
\[ \alpha = \frac{I_C}{I_E} \]
where \( I_C \) is the collector current and \( I_E \) is the emitter current.
- The current amplification factor `beta` (β) for a common emitter configuration is defined as:
\[ \beta = \frac{I_C}{I_B} \]
where \( I_B \) is the base current.

2. **Relate Emitter Current to Collector and Base Currents**:
- The relationship between the emitter current, collector current, and base current is given by:
\[ I_E = I_C + I_B \]

3. **Express Emitter Current in Terms of Collector Current**:
- Rearranging the above equation gives:
\[ I_E = I_C + \frac{I_C}{\beta} \quad (\text{since } I_B = \frac{I_C}{\beta}) \]
- Thus:
\[ I_E = I_C \left(1 + \frac{1}{\beta}\right) \]

4. **Substituting into the Definition of Alpha**:
- We can now express α in terms of β:
\[ \alpha = \frac{I_C}{I_E} = \frac{I_C}{I_C \left(1 + \frac{1}{\beta}\right)} = \frac{1}{1 + \frac{1}{\beta}} = \frac{\beta}{\beta + 1} \]

5. **Finding Relationships**:
- Rearranging gives us:
\[ \beta = \frac{\alpha}{1 - \alpha} \]
- This indicates a relationship between α and β.

6. **Identifying the Incorrect Relation**:
- The question asks for the relation that is not correct. The derived relationships are:
- \( \beta = \frac{\alpha}{1 - \alpha} \)
- \( \beta = \frac{\alpha}{1 + \alpha} \) (this is incorrect)
- Therefore, the incorrect relation is:
\[ \beta = \frac{\alpha}{1 + \alpha} \]

### Conclusion:
The current amplification factor `alpha` of a common base transistor and the current amplification factor `beta` of a common emitter transistor are not related by:
\[ \beta = \frac{\alpha}{1 + \alpha} \]