Question

The correct relation between \(\alpha\) and \(\beta\) in a transistor is

• A. \(\beta = \frac{\alpha}{1 - \alpha}\)
• B. \(\beta = \frac{\alpha}{1 + \alpha}\)
• C. \(\beta = \frac{1 + \alpha}{\alpha}\)
• D. \(\beta = 1 - \alpha\)

Hint:

\(\alpha\) is common base current gain; \(\beta\) is common emitter current gain.

Answer 1

The Correct Option is B

Step 1: Concept:
\(\alpha = \frac{I_C}{I_E}\), \(\beta = \frac{I_C}{I_B}\), and \(I_E = I_B + I_C\).
Step 2: Explanation:
\(\beta = \frac{I_C}{I_B} = \frac{I_C}{I_E + I_C} = \frac{I_C/I_E}{1 + I_C/I_E} = \frac{\alpha}{1 + \alpha}\).
Step 3: Conclusion:
Thus, \(\beta = \frac{\alpha}{1 + \alpha}\).