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EEJ MAIN Physics QUESTION #7064
Question 1
In a common emitter configuration for a transistor, if $\alpha$ and $\beta$ represent the current gains in common base and common emitter modes respectively, identify the incorrect relationship between them.
  • $\alpha = \frac{\beta}{1-\beta}$✔️
  • $\alpha = \frac{\beta}{1+\beta}$
  • $\alpha = \frac{\beta^2}{1+\beta^2+2\beta}$
  • $\frac{1}{\alpha} = \frac{1}{\beta} + 1$
Correct Answer Explanation

The standard relation between $\alpha$ and $\beta$ is $\beta = \frac{\alpha}{1-\alpha}$, which can be rearranged to $\alpha = \frac{\beta}{1+\beta}$.

  • Option B is correct.
  • Option D is simply a rearranged form: $\frac{1}{\alpha} = \frac{1+\beta}{\beta} = \frac{1}{\beta} + 1$.
  • Option C is the square of Option B: $\alpha = \left(\frac{\beta}{1+\beta}\right)^2$. While not the standard linear relation, Option A is explicitly wrong because $\alpha$ must always be less than 1, and $\frac{\beta}{1-\beta}$ would result in a value greater than 1.