Common-base (CB) configuration: Given emitter current IE = 4.2 mA and collector current IC = 4.0 mA, what is the current gain α (alpha = IC / IE)?

Introduction:In a common-base BJT configuration, the relevant current gain is α (alpha), defined as the ratio of collector current to emitter current. This parameter is typically close to but less than 1. Calculating α from given currents reinforces current relationships in BJTs and complements the more familiar β in common-emitter circuits.

Given Data / Assumptions:

• IE = 4.2 mA (emitter current).
• IC = 4.0 mA (collector current).
• Steady-state operation, neglecting leakage for simplicity.

Concept / Approach:By definition, α = IC / IE. The conservation relation IE = IB + IC holds; thus α = 1 − (IB / IE). For a healthy transistor, IB is small compared to IE, so α approaches 1 but remains slightly less. We simply substitute the given values to compute α numerically.

Step-by-Step Solution:

Verification / Alternative check:From IE = IB + IC → IB = IE − IC = 0.2 mA. Then α = 1 − IB/IE = 1 − 0.2/4.2 ≈ 1 − 0.04762 = 0.95238, confirming the result.

Why Other Options Are Wrong:

• 16.80: Not dimensionally meaningful for this ratio; grossly incorrect.
• 1.05: α cannot exceed 1 in a normal BJT.
• 0.20: Would imply unrealistic base current comparable to emitter current.

Common Pitfalls:Confusing α with β (β = IC / IB) or mixing up which currents define the ratio. Always use α = IC / IE for common-base analysis.

Final Answer:0.95