Question

Define the current gain \( \alpha_{DC} \) and \( \beta_{DC} \) for a transistor. Obtain the relation between them.

Hint:

The current gain \( \beta_{DC} \) is related to \( \alpha_{DC} \) and represents the amplification factor in the common-emitter configuration.

Answer 1

For a transistor, the current gain \( \alpha_{DC} \) and \( \beta_{DC} \) are defined as:
\[ \alpha_{DC} = \frac{I_C}{I_E}, \quad \beta_{DC} = \frac{I_C}{I_B} \] where \( I_C \) is the collector current, \( I_E \) is the emitter current, and \( I_B \) is the base current.
The relation between \( \alpha_{DC} \) and \( \beta_{DC} \) is given by:
\[ \beta_{DC} = \frac{\alpha_{DC}}{1 - \alpha_{DC}} \]