The current gain `beta` may be defined as

Options

A. the ratio of change in collector current to the change in emitter current for a constant collector voltage in a common base arrangement.
B. the ratio of change in collector current to the change in the base current at constant collector voltage in a common emitter circuit
C. the ratio of change in emitter current to the change in base current for constant emitter voltage in common emitter circuit.
D. the ratio of change in base current to the change in collector current at constant collector voltage in common emitter circuit.

Answer

To define the current gain \( \beta \) in a transistor, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Transistor Configuration**:
- A transistor has three terminals: the emitter (E), the base (B), and the collector (C). The currents flowing through these terminals are denoted as \( I_E \) (emitter current), \( I_B \) (base current), and \( I_C \) (collector current).

2. **Defining the Current Gain \( \beta \)**:
- The current gain \( \beta \) is a measure of how much the collector current \( I_C \) is amplified compared to the base current \( I_B \). It is defined mathematically as:
\[ \beta = \frac{I_C}{I_B} \]

3. **Analyzing the Options**:
- We need to analyze the given options to see which one correctly describes \( \beta \):
- **Option A**: Ratio of change in collector current to the change in emitter current for constant flow.
- **Option B**: Ratio of change in collector current to the change in base current at constant voltage.

4. **Evaluating the Options**:
- **Option A** is incorrect because \( \beta \) does not relate the collector current to the emitter current.
- **Option B** is correct because it describes the relationship between the collector current and the base current, which is what \( \beta \) represents.

5. **Conclusion**:
- The correct definition of the current gain \( \beta \) is:
\[ \beta = \frac{I_C}{I_B} \]
- Therefore, the correct option is **Option B**.