Question

For a transistor, $\alpha_{dc}$ and $\beta_{dc}$ are the current ratios, then the value of $\frac{\beta_{dc}-\alpha_{dc}}{\alpha_{dc}\times\beta_{dc}}$ is}

• A. 2.5
• B. 2
• C. 1.5
• D. 1

Hint:

Always remember $\beta$ is usually much larger than $\alpha$.

Answer 1

The Correct Option is D

Step 1: Formula
The relationship between $\alpha$ and $\beta$ is $\beta = \frac{\alpha}{1-\alpha}$ and $\alpha = \frac{\beta}{1+\beta}$.

Step 2: Analysis
We need to simplify the expression: $\frac{\beta - \alpha}{\alpha \beta}$.
$\frac{\beta - \alpha}{\alpha \beta} = \frac{\beta}{\alpha \beta} - \frac{\alpha}{\alpha \beta} = \frac{1}{\alpha} - \frac{1}{\beta}$.

Step 3: Calculation
Substitute $\frac{1}{\alpha} = \frac{1+\beta}{\beta}$:
$\frac{1+\beta}{\beta} - \frac{1}{\beta} = \frac{1+\beta-1}{\beta} = \frac{\beta}{\beta} = 1$.

Step 4: Conclusion
Hence, the value of the expression is 1. Final Answer: (D)