Load-line analysis in a BJT amplifier: at cutoff (no collector current), where is the Q-point located on the DC load line?

Introduction / Context:
In transistor biasing, the quiescent operating point (Q-point) determines linearity and headroom. The DC load line graphically relates the collector current and collector-emitter voltage for a given collector resistor and supply. Understanding where the Q-point sits in cutoff and saturation helps with quick reasoning about amplifier states and troubleshooting bias problems.

Given Data / Assumptions:

• Common-emitter configuration with supply voltage V_CC and collector resistor R_C.
• Cutoff means base current is essentially zero and collector current I_C ≈ 0.
• The DC load line extends from (I_C = 0, V_CE = V_CC) to (I_C = V_CC / R_C, V_CE = 0).

Concept / Approach:
Cutoff corresponds to no conduction through the transistor. If I_C ≈ 0, then the voltage drop across R_C is I_C * R_C ≈ 0 and the collector-emitter voltage rises to nearly V_CC. On the I_C–V_CE axes, this is the bottom-right or “lower-end” point at I_C = 0 and V_CE = V_CC on the load line.

Step-by-Step Solution:
Recognize cutoff: base drive absent → I_C ≈ 0.Compute V_CE at I_C = 0: V_CE ≈ V_CC (maximum).Locate on load line: point at the I_C = 0 intercept.Identify this as the lower end of the plotted line if current is the vertical axis.

Verification / Alternative check:
Oscilloscope or curve tracer plots show that as bias is reduced, the operating point slides toward I_C = 0 along the same load line; measured V_CE approaches V_CC, confirming the cutoff location.

Why Other Options Are Wrong:
Upper end corresponds to saturation (I_C maximum, V_CE near 0). Middle is quiescent for symmetrical swing but not cutoff. “Infinity” has no meaning on the finite load line. “None” is wrong since the lower end is correct.

Common Pitfalls:
Reversing axis interpretations; forgetting that terms “upper”/“lower” depend on convention—here “lower end” refers to the end with zero I_C.

Final Answer:
lower end of the load line