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: Write the gains.
For a transistor, $\alpha = \tfrac{I_C}{I_E}$ and $\beta = \tfrac{I_C}{I_B}$, with the current rule $I_E = I_C + I_B$.

Step 2: Flip the gains.
So $\tfrac{1}{\alpha} = \tfrac{I_E}{I_C}$ and $\tfrac{1}{\beta} = \tfrac{I_B}{I_C}$.

Step 3: Subtract.
\[ \frac{1}{\alpha} - \frac{1}{\beta} = \frac{I_E - I_B}{I_C}. \] Since $I_E - I_B = I_C$, this is $\tfrac{I_C}{I_C}$.

Step 4: Final value.
\[ \boxed{1} \]