Question

For a transistor, $\frac{1}{\alpha_{DC}} - \frac{1}{\beta_{DC}}$ is equal to [$\alpha_{DC}$ and $\beta_{DC}$ are current amplification factors]

• A. three
• B. two
• C. zero
• D. one

Hint:

Always remember the basic current relation for a transistor: the emitter current is the sum of collector and base currents ($I_E = I_C + I_B$). This relationship is the key to deriving most transistor gain formulas.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks to evaluate the expression $\frac{1}{\alpha_{DC}} - \frac{1}{\beta_{DC}}$ using transistor current gain relationships.

Step 2: Key Formula or Approach:
Use the relations $\alpha = \frac{I_C}{I_E}$ and $\beta = \frac{I_C}{I_B}$, where $I_E = I_C + I_B$.

Step 3: Detailed Explanation:
1. We know $\alpha = \frac{I_C}{I_E}$ and $\beta = \frac{I_C}{I_B}$.
2. The expression is $\frac{1}{\alpha} - \frac{1}{\beta} = \frac{I_E}{I_C} - \frac{I_B}{I_C}$.
3. Since $I_E = I_C + I_B$, we can write $I_E - I_B = I_C$.
4. Substituting this into the expression: $\frac{I_E - I_B}{I_C} = \frac{I_C}{I_C} = 1$.

Step 4: Final Answer:
The value of the expression is one, which corresponds to option (D).