Question

For a common emitter configuration, if '$\alpha$' and '$\beta$' have their usual meanings, the incorrect relation between '$\alpha$' and '$\beta$' is

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

Hint:

Physics Tip: Because the collector current is always slightly less than the emitter current, $\alpha$ is always slightly less than 1, whereas $\beta$ is usually much larger than 1.

Answer 1

The Correct Option is B

Concept: Physics (Semiconductors) - Transistor Parameters $\alpha$ and $\beta$.

Step 1: Recall the standard relationships. In a transistor, $\alpha$ is the current gain in a common base configuration and $\beta$ is the current gain in a common emitter configuration. They are related by: $$ \beta = \frac{\alpha}{1 - \alpha} \text{ and } \alpha = \frac{\beta}{1 + \beta} $$

Step 2: Test the given options.
• Option A: $\frac{1}{\alpha} = \frac{1}{\beta} + 1 \implies \frac{1}{\alpha} = \frac{1 + \beta}{\beta} \implies \alpha = \frac{\beta}{1 + \beta}$. This is correct.
• Option C: $\alpha = \frac{\beta}{1 + \beta}$. This is the standard correct relation.
• Option D: $\frac{1}{\beta} = \frac{1}{\alpha} - 1 \implies \frac{1}{\beta} = \frac{1 - \alpha}{\alpha} \implies \beta = \frac{\alpha}{1 - \alpha}$. This is correct.

Step 3: Identify the incorrect option. Option B states $\alpha = \frac{\beta}{1 - \beta}$, which does not match the established relationship $\alpha = \frac{\beta}{1 + \beta}$. $$ \therefore \text{Option B is the incorrect relation.} $$