Node-voltage relation in a BJT: Using consistent polarities, is the collector–emitter voltage related to the other two junction voltages by V_CE = V_CB + V_BE?

Introduction / Context:
Voltages between pairs of nodes in a three-terminal device are not independent; they are linked by Kirchhoff’s Voltage Law (KVL). In a BJT, the three relevant terminal-to-terminal voltages are V_BE, V_CB, and V_CE. With a consistent sign convention, these obey a simple identity that is frequently used in analysis, bias design, and measurement interpretation.

Given Data / Assumptions:

• Terminals: base (B), collector (C), emitter (E).
• Voltage definitions: V_XY means V_X − V_Y.
• Consistent polarity across all definitions.

Concept / Approach:
By definition, V_CE = V_C − V_E. Also, V_CB = V_C − V_B and V_BE = V_B − V_E. Adding V_CB and V_BE gives (V_C − V_B) + (V_B − V_E) = V_C − V_E = V_CE. This is a pure algebraic identity derived from KVL and node-voltage definitions, independent of device region (cutoff, active, or saturation). It is widely used when converting between measured junction voltages and the overall collector–emitter voltage.

Step-by-Step Solution:

Verification / Alternative check:
Measure any two of the three voltages on a bench; computing the third with this relation matches the direct measurement (within meter resolution and wiring drops).

Why Other Options Are Wrong:
Device polarity (NPN/PNP), operating region, or the approximate 0.7 V diode drop do not alter the algebraic identity.

Common Pitfalls:
Mixing sign conventions (e.g., using V_EB instead of V_BE) and then adding without flipping signs; ensure consistent “from–to” ordering.

Final Answer:
Correct