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In a bipolar junction transistor (BJT), if the common-base current gain is α = 0.98, determine the corresponding common-emitter current gain β.

Difficulty: Easy

49
4.9
0.5
48
0.02

Correct Answer: 49

Explanation:

Introduction / Context:
This problem checks fundamental BJT relationships between the common-base current gain (alpha, written as α) and the common-emitter current gain (beta, written as β). Knowing how to convert between α and β is essential for circuit analysis, bias design, and interpreting datasheets.

Given Data / Assumptions:

Common-base current gain α = 0.98.
Standard BJT relations hold for a properly biased transistor in active region.
Leakage currents are neglected (typical assumption for basic calculations).

Concept / Approach:
In BJTs, the two gains are linked by the identities: β = α / (1 − α) and α = β / (1 + β). With α very close to 1, small changes in α lead to large changes in β. We directly apply the conversion formula to compute β from the given α value.

Step-by-Step Solution:

Start with the standard relation: β = α / (1 − α).Substitute α = 0.98: β = 0.98 / (1 − 0.98).Compute denominator: 1 − 0.98 = 0.02.Evaluate: β = 0.98 / 0.02 = 49.Hence, the common-emitter gain is β = 49.

Verification / Alternative check:

Use the inverse relation α = β / (1 + β). With β = 49, α = 49 / 50 = 0.98, which matches the given α. This confirms consistency.

Why Other Options Are Wrong:

4.9: Off by a factor of 10, likely a decimal slip.0.5 or 0.02: These are much too small for α close to 1.48: Close, but not exact; correct computation yields 49.

Common Pitfalls:

Confusing α with β directly or using β = 1 − α (incorrect). Always apply β = α / (1 − α).

In a bipolar junction transistor (BJT), if the common-base current gain is α = 0.98, determine the corresponding common-emitter current gain β.

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