Before You Begin

Question #43883

Difficulty: 8/10 | 🟢 Free

The Question

An AC voltage source $V(t) = V_0 \sin(\omega t)$ is connected in series with a resistor $R$ and a symmetric Zener clipper. The clipper consists of two identical Zener diodes connected back-to-back. Each Zener diode has a breakdown voltage $V_Z = V_0 / 2$ , an ideal forward bias characteristic (zero voltage drop and zero resistance), and a constant dynamic resistance $r_z = R$ in the reverse breakdown region. Before breakdown, the reverse resistance is infinite. If $V_0 = 200\text{ V}$ and $R = 50\ \Omega$ , calculate the average power dissipated in the Zener clipper over one complete cycle.

Options

A.
$\left( \frac{100}{3} + \frac{50\sqrt{3}}{\pi} \right)\text{ W}$
B.
$\left( \frac{400}{3} - \frac{100\sqrt{3}}{\pi} \right)\text{ W}$
C.
$\left( 100 - \frac{150\sqrt{3}}{\pi} \right)\text{ W}$
D.
$\left( \frac{200}{3} + \frac{100\sqrt{3}}{\pi} \right)\text{ W}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Series LCR Impedance Vector|Dynamic Resistance (AC Resistance)|Load Line Analysis|Zener vs Avalanche Breakdown

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze non-linear, time-varying circuits, specifically targeting the misconception that standard LTI (Linear Time-Invariant) phasor analysis can be applied universally.

Students often fall into the trap of calculating a static RMS voltage and dividing by a constant impedance.

However, the Zener diode's dynamic resistance ( $r_z$ ) only engages during the breakdown region, causing harmonic distortion and making the effective impedance a function of the conduction angle.

To solve this, students must abandon static phasor algebra, determine the specific phase interval where clipping occurs (Load Line Analysis), and integrate the instantaneous power over that exact conduction angle.

Distractor options represent the total power supplied by the source and the power dissipated solely in the series resistor, punishing students who fail to isolate the Zener clipper's specific energy dissipation.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Alternating Current - Class 12
Concept	Series LCR Impedance Vector
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free