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Question #43896

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The Question

A circuit consists of a cell (electromotive force $E = 10 \text{ V}$ , internal resistance $r = 1 \text{ }\Omega$ ), a switch $S$ , an inductor of inductance $L = 10 \text{ H}$ , and a resistor of resistance $R = 4 \text{ }\Omega$ all connected in series. A Zener diode with a reverse breakdown voltage $V_Z = 20 \text{ V}$ is connected in parallel across the switch $S$ . The cathode of the Zener diode is connected to the node between the cell's positive terminal and the switch. The switch $S$ is initially closed for a long time, allowing the current to reach a steady state. At $t = 0$ , the switch $S$ is suddenly opened. Assuming the Zener diode enters avalanche breakdown instantly, calculate the time taken for the current in the circuit to drop to zero.

Options

A.
$2 \ln(2) \text{ s}$
B.
$2.5 \ln(2) \text{ s}$
C.
$2 \ln(1.5) \text{ s}$
D.
$2.5 \ln(1.5) \text{ s}$

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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

Zener vs Avalanche Breakdown|Cell EMF vs Terminal Voltage|Transient Current in RL Circuit

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous application of Kirchhoff's Voltage Law during a transient state involving a non-linear component (Zener diode).

The primary trap is twofold: First, students often memorize the standard RL discharge formula and incorrectly assume the cell is removed from the circuit when the switch opens, leading them to omit the cell's EMF $E$ from the discharge loop (Option C).

Second, candidates frequently neglect the internal resistance $r$ of the cell during the transient phase, assuming the total resistance is just the load $R$ (Option B).

Option D is chosen if both errors are made simultaneously.

The correct approach requires recognizing that the cell remains in the loop and its internal resistance continues to dissipate energy.

Quick Facts About This Question

Question Information

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