Current relationships in a BJT: Which expression correctly states the total emitter current in terms of the other two transistor currents?

Introduction:
Understanding the current relationships in a BJT is foundational for both DC biasing and small-signal analysis. Kirchhoff’s current law at the transistor's base–emitter–collector junctions gives a simple identity linking the three terminal currents: emitter, base, and collector.

Given Data / Assumptions:

• Conventional current directions: currents entering/leaving as defined in standard BJT models.
• Steady-state operation, neglecting leakage for clarity.
• Device not in breakdown.

Concept / Approach:
By device topology and charge flow, the emitter current equals the sum of base and collector currents. This holds across operating regions (cutoff excepted where all are approximately zero). The identity is frequently used to translate between α and β formulations and to compute bias currents.

Step-by-Step Solution:

Verification / Alternative check:
From α = I_C / I_E and β = I_C / I_B, it follows that I_E = I_B + I_C consistently. Experimental measurement of the three currents will show this sum to within leakage and measurement tolerance.

Why Other Options Are Wrong:

• IE – IC: This equals IB, not IE.
• IC + IE: Double counts IE; not a meaningful identity.
• IB – IC: Not a standard relation and often negative in forward-active operation.

Common Pitfalls:
Sign convention mistakes when using simulated current probes, or forgetting that leakage currents can slightly perturb the equality at very low currents.

Final Answer:
IB + IC