Difficulty: Easy
Correct Answer: 49
Explanation:
Introduction / Context:Common-base (CB) and common-emitter (CE) current gains (α and β) are related for a bipolar junction transistor. Converting between them is routine in circuit analysis and device modeling.
Given Data / Assumptions:
Concept / Approach:The exact relationship between CE and CB current gains is β = α / (1 − α). This follows from current relations in a BJT: IE = IC + IB, with α = IC / IE and β = IC / IB.
Step-by-Step Solution:
Step 1: Use β = α / (1 − α).Step 2: Substitute α = 0.98.Step 3: Compute denominator: 1 − 0.98 = 0.02.Step 4: β = 0.98 / 0.02 = 49.Verification / Alternative check:
Cross-check with inverse: α = β / (β + 1) = 49 / 50 ≈ 0.98, consistent.Why Other Options Are Wrong:
51 or 47 or 45: Do not satisfy α = β / (β + 1) near 0.98.0.98: That is α, not β.Common Pitfalls:
Using β ≈ α / (1 − α) but miscomputing the small denominator; forgetting that small α error produces large β change.Final Answer:
49
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