For transistor relation in current amplification factors is-

Options

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

Answer

To solve the question regarding the relationship between the current amplification factors (alpha and beta) in transistors, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Definitions**:
- In a transistor, the current amplification factors are defined as:
- \( \alpha \) (common base configuration) = \( \frac{I_C}{I_E} \)
- \( \beta \) (common emitter configuration) = \( \frac{I_C}{I_B} \)

2. **Express \( I_C \) in terms of \( \beta \)**:
- From the definition of \( \beta \):
\[ I_C = \beta I_B \]

3. **Substitute \( I_C \) into the \( \alpha \) equation**:
- Substitute \( I_C \) in the equation for \( \alpha \):
\[ \alpha = \frac{I_C}{I_E} = \frac{\beta I_B}{I_E} \]

4. **Relate \( I_B \) to \( I_E \) and \( I_C \)**:
- We know that:
\[ I_B = I_E - I_C \]
- Substitute this into the equation for \( \alpha \):
\[ \alpha = \frac{\beta (I_E - I_C)}{I_E} \]

5. **Substitute \( I_C \) in terms of \( \alpha \)**:
- From the definition of \( \alpha \), we can express \( I_C \) as:
\[ I_C = \alpha I_E \]
- Substitute this into the equation:
\[ \alpha = \frac{\beta (I_E - \alpha I_E)}{I_E} \]

6. **Simplify the equation**:
- Factor out \( I_E \):
\[ \alpha = \frac{\beta I_E (1 - \alpha)}{I_E} \]
- This simplifies to:
\[ \alpha = \beta (1 - \alpha) \]

7. **Rearrange to find the relationship between \( \alpha \) and \( \beta \)**:
- Rearranging gives:
\[ \alpha + \alpha \beta = \beta \]
- Factor out \( \alpha \):
\[ \alpha (1 + \beta) = \beta \]
- Thus:
\[ \alpha = \frac{\beta}{1 + \beta} \]

8. **Express \( \beta \) in terms of \( \alpha \)**:
- Rearranging the previous equation gives:
\[ \beta = \frac{\alpha}{1 - \alpha} \]

### Final Result:
The relationship between the current amplification factors \( \alpha \) and \( \beta \) is:
\[ \beta = \frac{\alpha}{1 - \alpha} \]