In a common base transistor circuit, `I_C` is the Output current and `I_E` is the input current. The current gain `alpha` is

Options

A. Greater than one
B. Less than one
C. Equal to one
D. None of these

Answer

To solve the problem regarding the current gain \( \alpha \) in a common base transistor circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Current Relationships**:
In a common base transistor configuration, we have three main currents:
- \( I_E \): Input current (Emitter current)
- \( I_C \): Output current (Collector current)
- \( I_B \): Base current

The relationship between these currents can be expressed as:
\[ I_E = I_B + I_C \]

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

3. **Analyzing the Current Gain**:
Since \( I_E \) is the sum of \( I_C \) and \( I_B \), we can rearrange the equation:
\[ I_C = I_E - I_B \]
This indicates that \( I_C \) is less than \( I_E \) because \( I_B \) is a positive quantity (the base current is always positive in active mode).

4. **Substituting into the Gain Equation**:
By substituting \( I_C \) in the gain equation, we get:
\[ \alpha = \frac{I_E - I_B}{I_E} \]
This can be simplified to:
\[ \alpha = 1 - \frac{I_B}{I_E} \]

5. **Conclusion about the Value of \( \alpha \)**:
Since \( I_B \) is always a positive value, \( \frac{I_B}{I_E} \) is also positive, which means:
\[ \alpha < 1 \]
Thus, the current gain \( \alpha \) in a common base transistor is always less than 1.

### Final Answer:
The current gain \( \alpha \) in a common base transistor circuit is less than 1.