For a transistor, in a common emitter arragement, the alternating current gain `beta` is given by

Options

A. `(DeltaI_C)/(DeltaI_B)]_(V_(CE))`
B. `(DeltaI_B)/(DeltaI_E)]_(V_(BE))`
C. `(DeltaI_B)/(DeltaI_C)]_(V_(CE))`
D. `(DeltaI_C)/(DeltaI_E)]_(V_(CE))`

Answer

To find the alternating current gain \( \beta \) for a transistor in a common emitter arrangement, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**: In a common emitter configuration, the emitter terminal is common to both the input and output circuits. The input is applied between the base and emitter, while the output is taken between the collector and emitter.

2. **Define the Parameters**:
- Let \( I_C \) be the change in collector current.
- Let \( I_B \) be the change in base current.
- The collector-emitter voltage \( V_{CE} \) is kept constant during this measurement.

3. **Write the Formula for \( \beta \)**: The alternating current gain \( \beta \) is defined as the ratio of the change in collector current to the change in base current:
\[ \beta = \frac{\Delta I_C}{\Delta I_B} \]
where \( \Delta I_C \) is the change in collector current and \( \Delta I_B \) is the change in base current.

4. **Interpret the Result**: This means that \( \beta \) indicates how much the collector current changes for a given change in base current, under the condition of constant collector-emitter voltage.

5. **Select the Correct Option**: Based on the definition, we can conclude that the correct option that matches our answer is the one that states \( \beta \) is the ratio of change in collector current to the change in base current at a constant collector-emitter voltage.

### Final Answer:
The alternating current gain \( \beta \) in a common emitter arrangement is given by:
\[ \beta = \frac{\Delta I_C}{\Delta I_B} \quad \text{(at constant } V_{CE}\text{)} \]