Transistor terminal voltages and KVL: Is the collector–emitter voltage equal to the sum of the base–emitter voltage and the collector–base voltage (VCE = VBE + VCB)?

Introduction / Context:
Voltage relationships in three-terminal devices follow directly from Kirchhoff’s Voltage Law (KVL). Understanding how terminal voltages relate helps prevent sign errors and supports accurate bias analysis of BJTs in any operating region.

Given Data / Assumptions:

• Standard sign convention: terminal voltages referenced from the first terminal to the second (e.g., VXY = VX − VY).
• Device can be NPN or PNP; the identity is algebraic and independent of polarity choices.
• No special operating region restrictions are required.

Concept / Approach:
By definition, VCE = VC − VE. Also, VBE = VB − VE and VCB = VC − VB. Summing VBE + VCB yields (VB − VE) + (VC − VB) = VC − VE, which equals VCE. Thus, VCE = VBE + VCB is an identity derived from definitions, not an approximation, and holds in cutoff, active, or saturation regions as long as consistent sign conventions are used.

Step-by-Step Solution:

Verification / Alternative check:
Apply KVL around the triangle formed by the three terminals; the algebraic sum is zero, leading to the same identity.

Why Other Options Are Wrong:

Common Pitfalls:
Mixing up sign conventions (e.g., VEB vs VBE) and then concluding the identity fails; always be consistent.

Final Answer:
Correct