Difficulty: Easy
Correct Answer: 3 mA
Explanation:
Introduction / Context:
In the common-emitter (C-E) configuration of a bipolar junction transistor (BJT), small changes in base current control much larger changes in collector current. The proportionality factor is the small-signal or DC current gain beta (β), making this relationship a staple of analog electronics and bias design.
Given Data / Assumptions:
Concept / Approach:
The core relationship for a BJT in active mode is Ic = β * Ib. With β specified and Ib known, Ic follows by direct multiplication. This linear approximation is widely used for first-pass bias calculations before more detailed modeling (e.g., Early effect) is applied.
Step-by-Step Solution:
1) Write the relationship: Ic = β * Ib.2) Substitute β = 100 and Ib = 30 µA.3) Calculate: Ic = 100 * 30 µA = 3000 µA.4) Convert units: 3000 µA = 3 mA.
Verification / Alternative check:
A quick unit sense-check: for β ≈ 100, collector current is roughly two orders of magnitude larger than base current. 30 µA * 100 = 3000 µA, which is 3 mA—consistent and reasonable for small-signal devices.
Why Other Options Are Wrong:
30 µA and 0.3 µA: These ignore the gain β (underestimate Ic heavily).
3 MA: Megaampere is absurdly large for a small-signal transistor—unit error by a factor of 10^6.
300 µA: This corresponds to β = 10, not 100.
Common Pitfalls:
Confusing β with α (common-base gain), mixing up microampere and milliampere units, or applying the formula outside the active region (near saturation where Ic no longer equals β * Ib). Always verify region of operation when finalizing a bias network.
Final Answer:
3 mA
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