Current gain in common-base configuration in less than `1`, because :

Options

A. `I_(e) lt I_(p)`
B. `I_(p) lt I_(e)`
C. `I_(c) lt I_(e)`
D. ` I_(e) lt I_(c)`

Answer

To solve the question regarding why the current gain in a common-base configuration is less than 1, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- In a common-base configuration, the base terminal of the transistor (NPN or PNP) is common to both the input and output circuits. The input current is supplied to the emitter, and the output current is taken from the collector.

2. **Current Relationships**:
- The relationship between the emitter current (IE), base current (IB), and collector current (IC) is given by the equation:
\[ I_E = I_B + I_C \]
- This equation indicates that the emitter current is the sum of the base current and the collector current.

3. **Inequalities**:
- From the equation \( I_E = I_B + I_C \), we can deduce that:
\[ I_E > I_B \quad \text{and} \quad I_E > I_C \]
- This means that the emitter current is always greater than both the base current and the collector current.

4. **Defining Current Gain**:
- The current gain (α) in a common-base configuration is defined as the ratio of the collector current (IC) to the emitter current (IE):
\[ \alpha = \frac{I_C}{I_E} \]

5. **Analyzing the Gain**:
- Since we established that \( I_E > I_C \), we can conclude:
\[ I_C < I_E \]
- Therefore, when we take the ratio:
\[ \frac{I_C}{I_E} < 1 \]
- This implies that the current gain (α) is always less than 1.

6. **Conclusion**:
- The current gain in a common-base configuration is less than 1 because the emitter current (IE) is always greater than the collector current (IC).

### Final Answer:
The current gain in a common-base configuration is less than 1 because the collector current (IC) is always less than the emitter current (IE).