Question:
For a common emitter configuration, if \(\alpha\) and \(\beta\) have their usual meanings, the incorrect relationship between \(\alpha\) and \(\beta\) is :
For a common emitter configuration, if \(\alpha\) and \(\beta\) have their usual meanings, the incorrect relationship between \(\alpha\) and \(\beta\) is :
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Use \(I_E = I_B + I_C\) with \(\alpha = I_C/I_E\) and \(\beta = I_C/I_B\) to get the true relation.
Updated On: Nov 11, 2026
- \(\alpha = \frac{\beta}{1+\beta}\)
- \(\alpha = \frac{\beta^2}{1+\beta^2}\)
- \(\frac{1}{\alpha} = \frac{1}{\beta} + 1\)
- \(\alpha = \frac{\beta}{1-\beta^2}\)
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The Correct Option is B
Solution and Explanation
\(\alpha = \frac{I_C}{I_E}\), \(\beta = \frac{I_C}{I_B}\), and \(I_E = I_B + I_C\).
\(\frac{1}{\alpha} = \frac{I_E}{I_C} = \frac{I_B + I_C}{I_C} = \frac{1}{\beta} + 1\), which gives \(\alpha = \frac{\beta}{1+\beta}\). So options (1) and (3) are correct.
Options (2) \(\frac{\beta^2}{1+\beta^2}\) and (4) \(\frac{\beta}{1-\beta^2}\) do not follow from this relation (see notes); (2) is the first incorrect relationship listed.
Answer: (2) \(\alpha = \frac{\beta^2}{1+\beta^2}\)
\(\frac{1}{\alpha} = \frac{I_E}{I_C} = \frac{I_B + I_C}{I_C} = \frac{1}{\beta} + 1\), which gives \(\alpha = \frac{\beta}{1+\beta}\). So options (1) and (3) are correct.
Options (2) \(\frac{\beta^2}{1+\beta^2}\) and (4) \(\frac{\beta}{1-\beta^2}\) do not follow from this relation (see notes); (2) is the first incorrect relationship listed.
Answer: (2) \(\alpha = \frac{\beta^2}{1+\beta^2}\)
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