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Question #43457

Difficulty: 8/10 | 🟢 Free

The Question

A common-emitter amplifier uses an NPN transistor. A potentiometer of length $L = 100 \text{ cm}$ is connected across a $V_0 = 2.0 \text{ V}$ DC supply. The wiper, positioned at a distance $x$ from the grounded end, provides the DC bias voltage $V_{BE}$ to the transistor. The collector is connected to a $V_{CC} = 12 \text{ V}$ supply via a load resistor $R_C = 500 \ \Omega$ .

The collector current $I_C$ (in mA) varies with $V_{BE}$ (in V) according to the empirical relation: $I_C(V_{BE}) = 4.0 + 60(V_{BE} - 0.7) - 2000(V_{BE} - 0.7)^3$ for the range $0.6 \le V_{BE} \le 0.8 \text{ V}$ .

A small time-varying signal $v_i(t)$ is superimposed on the DC bias $V_{BE}$ . Assuming the base current drawn by the transistor is negligible compared to the current in the potentiometer, determine the wiper position $x$ that biases the transistor for maximum small-signal voltage gain, and the magnitude of this maximum gain $|A_v|$ .

Options

A.
$x = 35 \text{ cm}, |A_v| = 30$
B.
$x = 35 \text{ cm}, |A_v| = 30000$
C.
$x = 40 \text{ cm}, |A_v| = 0$
D.
$x = 65 \text{ cm}, |A_v| = 30$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Transistor Configuration Gains|Graphical Concavity Significance|Potentiometer Sensitivity

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of small-signal analysis and the physical meaning of transconductance ( $g_m$ ) as the derivative of the transfer characteristic.

A common trap is confusing the macroscopic DC operating point ( $I_C/V_{BE}$ ) with the dynamic AC gain ( $dI_C/dV_{BE}$ ), or incorrectly maximizing the collector current $I_C$ instead of its slope.

By requiring the identification of the inflection point ( $d^2I_C/dV_{BE}^2 = 0$ ) to maximize sensitivity, the problem separates rote memorization of the linear $\beta$ model from a true calculus-based understanding of non-linear circuit dynamics.

Furthermore, it tests dimensional vigilance by mixing mA/V with Ohms.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Semiconductor Electronics: Materials, Devices, and Simple Circuits - Class 12
Concept	Transistor Configuration Gains
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free