Question

For a transistor if \(\alpha = 0.98\) and emitter current is \(2.8\,mA\), then the collector current is

• A. \(0.44\,mA\)
• B. \(0.88\,mA\)
• C. \(2.74\,mA\)
• D. \(3.32\,mA\)

Hint:

\(\alpha\) is ratio of collector to emitter current.

Answer 1

The Correct Option is C

Step 1: Convert $\alpha$ to $\beta$.
The current gain $\alpha$ and $\beta$ are related by $\beta = \dfrac{\alpha}{1-\alpha}$. With $\alpha = 0.98$: $\beta = \dfrac{0.98}{1-0.98} = \dfrac{0.98}{0.02} = 49$.

Step 2: Find base current from emitter current.
In a BJT, $I_E = I_B + I_C = I_B(1+\beta)$. So $I_B = \dfrac{I_E}{1+\beta} = \dfrac{2.8}{50} = 0.056\,mA$.

Step 3: Compute collector current.
$I_C = \beta \times I_B = 49 \times 0.056 = 2.744\,mA \approx 2.74\,mA$. \[ \boxed{2.74\,mA} \]