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Question #43880

Difficulty: 8/10 | 🟢 Free

The Question

A voltage regulator circuit consists of a DC voltage source $V_S = 15.0 \text{ V}$ , a series linear resistor $R = 200 \ \Omega$ , and a semiconductor diode operating at the boundary of Zener and Avalanche breakdown. At the steady-state operating point, the voltage across the diode is $V_Z = 5.0 \text{ V}$ . Due to the non-linear tunneling and ionization dynamics at the breakdown knee, the diode exhibits a dynamic (differential) resistance $r_d = 50 \ \Omega$ at this specific operating point. If the source voltage undergoes a very small quasi-static fluctuation $dV_S$ , what is the rate of change of the power dissipated by the diode with respect to the source voltage, $\frac{dP_Z}{dV_S}$ , at this operating point? Assume the series resistor $R$ is strictly linear and phase-invariant.

Options

A.
30 \text{ mW/V}
B.
25 \text{ mW/V}
C.
$\frac{100}{3} \text{ mW/V}$
D.
20 \text{ mW/V}

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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

Resistor Phase Invariance|Load Line Analysis|Zener vs Avalanche Breakdown

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between static and dynamic (differential) resistance during Load Line Analysis of non-linear semiconductor devices.

A common trap for JEE Advanced candidates is treating a Zener diode in breakdown as an ideal voltage source ( $r_d = 0$ ), which incorrectly yields $dP_Z/dV_S = V_Z/R = 25 \text{ mW/V}$ .

Another trap is using the static resistance ( $R_Z = V_Z/I_Z = 100 \ \Omega$ ) instead of the dynamic resistance ( $r_d = 50 \ \Omega$ ) for small-signal variations, yielding $33.3 \text{ mW/V}$ .

The problem forces students to recognize that while the series resistor is phase-invariant and linear, the stability criterion ( $dI/dV$ ) at the breakdown knee strictly depends on the differential resistance $r_d = dV_Z/dI_Z$ , requiring a full differential analysis of the power equation $P_Z = V_Z I_Z$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Alternating Current - Class 12
Concept	Resistor Phase Invariance
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free