For a transistor `(I_(C))/(I_(E))=0.96`, then current gain for common emitter configuration

Options

A. 6
B. 12
C. 24
D. 48

Answer

To find the current gain (β) for a common emitter configuration of a transistor given that \(\frac{I_C}{I_E} = 0.96\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- We know that \(\frac{I_C}{I_E} = 0.96\). This ratio is defined as \(\alpha\), the current amplification factor in the common base configuration.

2. **Define the relationship between α and β:**
- The current gain in the common emitter configuration is defined as:
\[ \beta = \frac{I_C}{I_B} \]
- We also know that:
\[ I_E = I_B + I_C \]
- Rearranging gives:
\[ I_B = I_E - I_C \]

3. **Express β in terms of α:**
- Substituting \(I_B\) into the equation for β:
\[ \beta = \frac{I_C}{I_E - I_C} \]
- Now, we can express \(I_E\) in terms of \(I_C\) using the relationship with α:
\[ I_E = \frac{I_C}{\alpha} \]

4. **Substituting α into the equation for β:**
- Now substituting \(I_E\) into the β equation:
\[ \beta = \frac{I_C}{\frac{I_C}{\alpha} - I_C} \]
- Simplifying the denominator:
\[ \beta = \frac{I_C}{\frac{I_C - \alpha I_C}{\alpha}} = \frac{I_C \cdot \alpha}{I_C(1 - \alpha)} = \frac{\alpha}{1 - \alpha} \]

5. **Substituting the value of α:**
- Now substituting \(\alpha = 0.96\):
\[ \beta = \frac{0.96}{1 - 0.96} = \frac{0.96}{0.04} \]

6. **Calculating β:**
- Performing the division:
\[ \beta = 24 \]

### Final Answer:
The current gain for the common emitter configuration is \( \beta = 24 \).