Question:
The correct relation between \(\alpha\) and \(\beta\) in a transistor is
The correct relation between \(\alpha\) and \(\beta\) in a transistor is
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\(\alpha\) is common base current gain; \(\beta\) is common emitter current gain.
Updated On: Apr 23, 2026
- \(\beta = \frac{\alpha}{1 - \alpha}\)
- \(\beta = \frac{\alpha}{1 + \alpha}\)
- \(\beta = \frac{1 + \alpha}{\alpha}\)
- \(\beta = 1 - \alpha\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
\(\alpha = \frac{I_C}{I_E}\), \(\beta = \frac{I_C}{I_B}\), and \(I_E = I_B + I_C\).
Step 2: Detailed 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: Final Answer:
Thus, \(\beta = \frac{\alpha}{1 + \alpha}\).
\(\alpha = \frac{I_C}{I_E}\), \(\beta = \frac{I_C}{I_B}\), and \(I_E = I_B + I_C\).
Step 2: Detailed 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: Final Answer:
Thus, \(\beta = \frac{\alpha}{1 + \alpha}\).
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