Definition check: In a BJT, which current ratio defines the common-emitter current gain β (beta)?

Introduction:
Two current gains are frequently used to characterize BJTs: α (common-base) and β (common-emitter). Correctly identifying which ratio defines β is essential for circuit calculations, bias design, and interpreting datasheets.

Given Data / Assumptions:

• BJT operating in forward-active region.
• Steady-state currents IB, IC, and IE well-defined.
• Neglect leakage currents for simplicity.

Concept / Approach:
By definition, β (beta) is the ratio of collector current to base current in the common-emitter configuration: β = IC / IB. It relates directly to how base drive controls collector current. The related common-base gain is α = IC / IE. These quantities are linked approximately by β = α / (1 − α) and α = β / (β + 1).

Step-by-Step Solution:

Verification / Alternative check:
From IE = IB + IC, derive α and β relationships to confirm consistency: β = α/(1 − α), demonstrating that the chosen ratio is coherent with transistor current laws.

Why Other Options Are Wrong:

• IC/IE: That is α, not β.
• IB/IE or IE/IB: Neither corresponds to standard current gains.

Common Pitfalls:
Mixing up α and β or forgetting that β can vary widely with current, temperature, and device type; design should not rely on a single β value without margin.

Final Answer:
IC/IB