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Question #43900

Difficulty: 8/10 | 🟢 Free

The Question

In a common-emitter amplifier circuit, the AC collector current is given by $i_c(t) = I_0 \sin(\omega t)$ , where $I_0$ is the peak current and $\omega$ is the angular frequency. The AC load connected to the collector is a series LCR circuit with resistance $R$ , inductance $L$ , and capacitance $C$ . Due to the complex impedance of the load, the dynamic operating point traces a closed elliptical locus in the $v_{ce}-i_c$ plane, where $v_{ce}$ is the AC collector-emitter voltage. What is the area of this elliptical locus?

Options

A.
$\pi I_0^2 \sqrt{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2}$
B.
$\pi I_0^2 \left| \omega L - \frac{1}{\omega C} \right|$
C.
$\pi I_0^2 R$
D.
$\frac{\pi I_0^2 R^2}{\sqrt{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2}}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Transistor Biasing Stability|Load Line Analysis|Series LCR Impedance Vector|Resistor Phase Invariance

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to transition from static DC load line analysis to dynamic AC load line analysis in the presence of complex impedance.

A common trap is assuming that the area of a closed loop in a conjugate variable plane (like $P-V$ or $B-H$ ) always represents real energy dissipation, leading students to incorrectly choose the resistive term (Option C).

Alternatively, students might treat the AC load line as a static vector and use the total impedance magnitude $|Z|$ (Option A).

In reality, the area of the $v-i$ locus represents the reactive power exchange.

The resistive component shears the ellipse but preserves its area (Cavalieri's principle), making the area strictly dependent on the reactive impedance.

Quick Facts About This Question

Question Information

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