If the current gain in CB configuration is 0.96, then the current gain in the CE configuration will be

Options

A. 24
B. 20
C. 16
D. 12

Explanation

To find the current gain in the Common Emitter (CE) configuration given the current gain in the Common Base (CB) configuration, we can use the relationship between the two current gains, alpha (α) and beta (β).

### Step-by-step Solution:

1. **Understand the Definitions:**
- In a transistor, the current gain in the 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 gain in the Common Emitter configuration is defined as:
\[ \beta = \frac{I_C}{I_B} \]
where \(I_B\) is the base current.

2. **Relationship Between α and β:**
- There is a relationship between α and β given by:
\[ \beta = \frac{\alpha}{1 - \alpha} \]

3. **Substituting the Given Value:**
- We are given that \( \alpha = 0.96 \).
- Substitute this value into the equation for β:
\[ \beta = \frac{0.96}{1 - 0.96} \]

4. **Calculate the Denominator:**
- Calculate \(1 - 0.96\):
\[ 1 - 0.96 = 0.04 \]

5. **Calculate β:**
- Now substitute the value of the denominator back into the equation for β:
\[ \beta = \frac{0.96}{0.04} \]

6. **Perform the Division:**
- Calculate \( \frac{0.96}{0.04} \):
\[ \beta = 24 \]

7. **Conclusion:**
- Therefore, the current gain in the Common Emitter configuration is:
\[ \beta = 24 \]

### Final Answer:
The current gain in the CE configuration is **24**.