Introduction / Context:
In a bipolar junction transistor operating in active region, the collector current is approximately β times the base current (neglecting I_CBO). This quick calculation is central to biasing and small-signal design estimates.
Given Data / Assumptions:
- β (DC current gain) = 125.
- I_B = 30 µA.
- Assume active region and negligible leakage currents.
Concept / Approach:
- Relation: I_C ≈ β * I_B.
- Convert microamps to milliamps for the final expression.
Step-by-Step Solution:
Compute product: I_C = 125 * 30 µA.Multiply: 125 * 30 = 3750 µA.Convert units: 3750 µA = 3.75 mA.
Verification / Alternative check:
Rough check: 100 * 30 µA = 3.0 mA; extra 25 * 30 µA = 0.75 mA; total 3.75 mA.
Why Other Options Are Wrong:
- 3.2 mA: Underestimates β * I_B.
- 0.05 mA: Off by orders of magnitude.
- 13 mA: Too high for given β and I_B.
- None of the above: Incorrect because 3.75 mA is correct.
Common Pitfalls:
- Mismatching units (µA vs mA).
- Using α (common-base gain) instead of β; here β relation is explicit.
Final Answer:
3.75 mA
Discussion & Comments